//
// Frink data file for non-changing units.
//
// This file is used by the Frink calculating tool/programming language:
// http://futureboy.homeip.net/frinkdocs/
//
// If you got to this page from a web search because you're trying to do a
// unit conversion or manipulation, try it at the following URL:
//
// http://futureboy.homeip.net/frink/
//
// Alan Eliasen
// eliasen@mindspring.com
//
//
// This file is adapted, modified, and extended from the units database for use
// with GNU units, a units conversion program by Adrian Mariano
// adrian@cam.cornell.edu, who did a damn fine job collecting much of this.
//
//
// Most units data was drawn from
// 1. NIST Special Publication 811, 1995 Edition
// 2. CRC Handbook of Chemistry and Physics 70th edition
// 3. Oxford English Dictionary
// 4. Websters New Universal Unabridged Dictionary
// 5. Units of Measure by Stephen Dresner
// 6. A Dictionary of English Weights and Measures by Ronald Zupko
// 7. British Weights and Measures by Ronald Zupko
// 8. Realm of Measure by Isaac Asimov
// 9. United States standards of weights and measures, their
// creation and creators by Arthur H. Frazier.
// 10. French weights and measures before the Revolution: a
// dictionary of provincial and local units by Ronald Zupko
// 11. Weights and Measures: their ancient origins and their
// development in Great Britain up to AD 1855 by FG Skinner
// 12. The World of Measurements by H. Arthur Klein
// 13. For Good Measure by William Johnstone
// 14. NTC's Encyclopedia of International Weights and Measures
// by William Johnstone
// 15. Sizes by John Lord
// 16. Sizesaurus by Stephen Strauss
// 17. CODATA Recommended Values of Physical Constants available at
// http://physics.nist.gov/cuu/Constants/index.html
//
// Thanks to Jeff Conrad for assistance in ferreting out unit definitions.
//
/////////////////////////////////////////////////////////////////////////////
// //
// Primitive units. Any unit defined to contain a '!' character is a //
// primitive unit which will not be reduced any further. All units should //
// reduce to primitive units. //
// //
/////////////////////////////////////////////////////////////////////////////
// Prefixes
// These are defined with the symbol :- to indicate a prefix which cannot
// stand by itself (must be attached to a unit)
// or with the symbol ::- for a prefix which can be either attached to a unit
// or defines a standalone unit.
//
// A number specifed like "1ee20" with integers for the factor and the
// exponent are treated as exact numbers.
yotta ::- 1ee24 // 1E24 Greek or Latin octo, "eight"
zetta ::- 1ee21 // 1E21 Latin septem, "seven"
exa ::- 1ee18 // 1E18 Greek hex, "six"
peta ::- 1ee15 // 1E15 Greek pente, "five"
tera ::- 1ee12 // 1E12 Greek teras, "monster"
giga ::- 1ee9 // 1E9 Greek gigas, "giant"
mega ::- 1ee6 // 1E6 Greek megas, "large"
myria ::- 1ee4 // 1E4 Not an official SI prefix
kilo ::- 1000 // 1E3 Greek chilioi, "thousand"
hecto ::- 100 // 1E2 Greek hekaton, "hundred"
deca ::- 10 // 1E1 Greek deka, "ten"
deka ::- 10
deci ::- 1/10 // 1E-1 Latin decimus, "tenth"
centi ::- 1/100 // 1E-2 Latin centum, "hundred"
milli ::- 1/1000 // 1E-3 Latin mille, "thousand"
micro ::- 1ee-6 // 1E-6 Latin micro/Greek mikros,"small"
nano ::- 1ee-9 // 1E-9 Latin nanus or Greek nanos,"dwarf"
pico ::- 1ee-12 // 1E-12 Spanish pico, "a bit"
femto ::- 1ee-15 // 1E-15 Danish-Norwegian femten,"fifteen"
atto ::- 1ee-18 // 1E-18 Danish-Norwegian atten,"eighteen"
zepto ::- 1ee-21 // 1E-21 Latin septem, "seven"
yocto ::- 1ee-24 // 1E-24 Greek or Latin octo, "eight"
Y :- yotta
Z :- zetta
E :- exa
P :- peta
T :- tera
G :- giga
M :- mega
k :- kilo
h :- hecto
da :- deka
d :- deci
c :- centi
m :- milli
// Alan's notes:
// I'd like to put a mu in here for micro.
// Should we adopt the questionable Electrical Engineer policy of using
// "u" to indicate micro? I've added "uF" for microfarad later on to
// tackle the most common case.
\u00b5 :- micro // Unicode "MICRO SIGN"
n :- nano
p :- pico
f :- femto
a :- atto
z :- zepto
y :- yocto
//
// SI units
//
length =!= m // Length of the path traveled by light in a vacuum
meter := m // during 1/299792458 seconds (exactly.)
// Originally meant to be one ten-millionth
// of the length along a meridian from the equator
// to a pole, but the measurement was off.
//
// Alan's notes:
// The earth's circumference would then be exactly 40
// million meters (which is a good thing to memorize.)
time =!= s // Duration of 9192631770 periods of the radiation
second := s // corresponding to the transition between the two hyperfine
// levels of the ground state of the cesium-133 atom
mass =!= kg // Mass of the international prototype, whatever that is.
//
// Alan's editorializing:
// I dislike having a prefixed unit as the base reference.
// What a horrible decision. Why don't you just have it go to
// ten and make ten a little louder?
kilogram := kg
gram := 1/1000 kg
currency =!= dollar// The US dollar is chosen arbitrarily to be the primitive
// unit of money. The dollar must be defined for use
// in the CPISource (providing historical purchasing power
// of the dollar) and for CurrencySource (providing
// exchange rate information
// (and things like the price of Gold)) so
// you can change the fundamental unit of currency, but you
// have to be able to turn it into a dollar if you want
// to use these other sources.
// If you want to define your own base currency, and you want
// currency conversions to still work, you
// should (for now) define the base currency as its 3-letter
// ISO-4217 currency code (say, "EUR" or "JPY"). This will
// allow the
// currency converter to unambiguously figure out which
// currency you mean. The units "Euro", "euro", the Euro
// symbol \u20ac, the Japanese Yen symbol \u00a5,
// the U.K. pound symbol \u0163, and "dollar" are
// special cases that also work.
//
// If you change your base currency, you might get a few
// errors about units below that are defined in terms of the
// dollar. You can probably comment those out and never miss
// them. If you have a 3-letter ISO code for your base
// currency, it'll figure out what a "dollar" is later, so
// you shouldn't need to hard-code in a conversion rate.
temperature =!= K // "1/273.16 of the thermodynamic temperature of the triple
kelvin := K // point of water." Note that there is a minor discrepancy
// between this value and the 273.15 K figure used to set
// the zero point of the Celsius scale. The *size* of a
// Kelvin or a degree Celsius is the same, but you need
// to remember that the offset point is slightly different.
// Use the Celsius[x] functions defined below to convert
// between these unit systems.
current =!= A // The current which produces a force of 2e-7 N/m between two
ampere := A // infinitely long wires that are 1 meter apart
amp := ampere
// Alan's editorializing:
// I'd actually much rather define this in terms of the charge
// of a fundamental particle. electroncharge/sec
// is less arbitrary. I'd actually prefer to have the base
// unit be charge instead of current.
substance =!= mol // The amount of substance of a system which contains as many
mole := mol // elementary entities as there are atoms in 0.012 kg of
// carbon 12. The elementary entities must be specified and
// may be atoms, molecules, ions, electrons, or other
// particles or groups of particles. It is understood that
// unbound atoms of carbon 12, at rest and in the ground
// state, are referred to.
//
// Alan's editorializing:
// As useful as a mole may be, I really think that a mole is
// insufficient by itself. It has to be a mole OF
// something. How do you represent that?
radian := 1 // The angle subtended at the center of a circle by an arc
// equal in length to the radius of the circle.
// A circle thus subtends an angle of 2 pi radians.
//
// Alan's editorializing:
// Despite what other units programs might have you believe,
// radians ARE dimensionless units and making them their own
// unit leads to all sorts of arbitrary convolutions in
// calculations (at the possible expense of some inclarity if
// you don't know what you're doing.)
// If you really want radians to be a fundamental unit,
// replace the above with "angle =!= radian"
// (This will give you a bit of artificiality in calculations.)
sr := 1 // Solid angle which cuts off an area of the surface of
steradian := sr// the sphere equal to that of a square with sides of
// length equal to the radius of the sphere.
// A sphere thus subtends 4 pi steradians.
// Also a dimensionless unit (length^2/length^2)
// If you really want steradians to be a fundamental unit,
// replace the above with "solid_angle =!= sr"
// (This will give you a bit of artificiality in calculations.)
information =!= bit// Basic unit of information (entropy). The entropy in bits
// of a random variable over a finite alphabet is defined
// to be the sum of -p(i)*log2(p(i)) over the alphabet where
// p(i) is the probability that the random variable takes
// on the value i.
//
// Alan's editorializing: That irrelevant non-sequitur
// about entropy isn't my doing. What does that have to
// do with the bit itself? I'm also considering changing
// bits to be dimensionless units--it makes problems in
// information theory come out more reasonably.
luminous_intensity =!= cd
candela := cd // Official definition:
// "The candela is the luminous intensity, in a given
// direction, of a source that emits monochromatic radiation
// of frequency 540 x 10^12 hertz and that has a radiant
// intensity in that direction of 1/683 watt per steradian."
//
// (This differs from radiant
// intensity (W/sr) in that it is adjusted for human
// perceptual dependence on wavelength. The frequency of
// 540e12 Hz (yellow) is where human perception is most
// efficient.)
//
// Alan's editorializing:
// I think the candela is a scam, and I am completely
// opposed to it. Some good-for-nothing lighting "engineers"
// or psychologists probably got this perceptually-rigged
// abomination into the whole otherwise scientific endeavor.
//
// What an unbelievably useless and stupid unit. Is light
// at 540.00000001 x 10^12 Hz (or any other frequency) zero
// candela? Is this expected to be an impulse function at
// this frequency? Oh, wait, the Heisenberg Uncertainty
// Principle makes this impossible. No mention for
// correction (ideally along the blackbody curve) for other
// wavelengths? Damn you, 16th CGPM! Damn you all to hell!
// Define the default symbol for the imaginary unit, that is, the square
// root of negative one.
i := <>
// Define unit combinations
1 ||| dimensionless
m^2 ||| area
m^3 ||| volume
s^-1 ||| frequency
m s^-1 ||| velocity
m s^-2 ||| acceleration
m kg s^-1 ||| momentum
m kg s^-2 ||| force
m^2 kg s^-3 ||| power
m^-1 kg s^-2 ||| pressure
m^2 kg s^-2 ||| energy
m^2 kg s^-1 ||| angular_momentum
m^2 kg ||| moment_of_inertia
m^3 s^-1 ||| flow
m^-3 kg ||| mass_density
m^3 kg ||| specific_volume
A m^-2 ||| electric_current_density
dollar kg^-1 ||| price_per_mass
//
// Names of some numbers
//
semi :- 1/2
demi :- 1/2
hemi :- 1/2
half ::- 1/2
third ::- 1/3
quarter ::- 1/4
eighth ::- 1/8
uni :- 1
bi :- 2
tri :- 3
one := 1
two := 2
double := 2
three := 3
triple := 3
treble := 3
four := 4
quadruple := 4
five := 5
quintuple := 5
six := 6
sextuple := 6
seven := 7
septuple := 7
eight := 8
nine := 9
ten := 10
twenty := 20
thirty := 30
forty := 40
fifty := 50
sixty := 60
seventy := 70
eighty := 80
ninety := 90
hundred := 100
thousand := 1000
million := 1ee6
billion := 1ee9
trillion := 1ee12
quadrillion := 1ee15
quintillion := 1ee18
sextillion := 1ee21
septillion := 1ee24
octillion := 1ee27
nonillion := 1ee30
noventillion := nonillion
decillion := 1ee33
undecillion := 1ee36
duodecillion := 1ee39
tredecillion := 1ee42
quattuordecillion := 1ee45
quindecillion := 1ee48
sexdecillion := 1ee51
septendecillion := 1ee54
octodecillion := 1ee57
novemdecillion := 1ee60
vigintillion := 1ee63
centillion := 1ee303
googol := 1ee100
// These number terms were described by N. Chuquet and De la Roche in the 16th
// century as being successive powers of a million. These definitions are
// still used in most European countries. The current US definitions for these
// numbers arose in the 17th century and don't make nearly as much sense.
// These numbers are listed in the CRC Concise Encyclopedia of Mathematics by
// Eric W. Weisstein.
brbillion := million^2
brtrillion := million^3
brquadrillion := million^4
brquintillion := million^5
brsextillion := million^6
brseptillion := million^7
broctillion := million^8
brnonillion := million^9
brnoventillion := brnonillion
brdecillion := million^10
brundecillion := million^11
brduodecillion := million^12
brtredecillion := million^13
brquattuordecillion := million^14
brquindecillion := million^15
brsexdecillion := million^16
brseptdecillion := million^17
broctodecillion := million^18
brnovemdecillion := million^19
brvigintillion := million^20
// These numbers fill the gaps left by the European system above.
milliard := 1000 million
billiard := 1000 million^2
trilliard := 1000 million^3
quadrilliard := 1000 million^4
quintilliard := 1000 million^5
sextilliard := 1000 million^6
septilliard := 1000 million^7
octilliard := 1000 million^8
nonilliard := 1000 million^9
noventilliard := nonilliard
decilliard := 1000 million^10
// For consistency
brmilliard := milliard
brbilliard := billiard
brtrilliard := trilliard
brquadrilliard := quadrilliard
brquintilliard := quintilliard
brsextilliard := sextilliard
brseptilliard := septilliard
broctilliard := octilliard
brnonilliard := nonilliard
brnoventilliard := noventilliard
brdecilliard := decilliard
// The British Centillion would be 1ee600. The googolplex is another
// familiar large number equal to 10^googol. These numbers give overflows.
//////////////////////////////////////////////////////////////////////////////
// //
// Derived units which can be reduced to the primitive units //
// //
//////////////////////////////////////////////////////////////////////////////
//
// Named SI derived units (officially accepted)
//
newton := kg m / s^2 // force
N := newton
pascal := N/m^2 // pressure or stress
Pa := pascal
joule := N m // energy
J := joule
watt := J/s // power
W := watt
J m^-2 ||| surface_tension
coulomb := A s // charge
coulomb ||| charge
coulomb m^-2 ||| surface_charge_density
coulomb m^-3 ||| electric_charge_density
C := coulomb
volt := W/A // potential difference
V := volt
volt ||| electric_potential
V / m ||| electric_field_strength
A / m ||| magnetic_field_strength
ohm := V/A // electrical resistance
\u2126 := ohm // Official Unicode codepoint OHM SIGN
\u03a9 := ohm // "Preferred" Unicode codepoint for ohm
// GREEK CAPITAL LETTER OMEGA
ohm ||| electric_resistance
siemens := A/V // electrical conductance
S := siemens
siemens ||| electric_conductance
farad := C/V // capacitance
farad ||| capacitance
F := farad
uF := microfarad // Concession to electrical engineers
// without adding the questionable "u"
// as a general prefix.
weber := V s // magnetic flux
weber ||| magnetic_flux
Wb := weber
henry := Wb/A // inductance
henry ||| inductance
henries := henry // Irregular plural
H := henry
tesla := Wb/m^2 // magnetic flux density
tesla ||| magnetic_flux_density
T := tesla
hertz := s^-1 // frequency
Hz := hertz
J/K ||| heat_capacity
J kg^-1 K^-1 ||| specific_heat_capacity
//
// time
//
sec := s
minute := 60 s
min := minute
hour := 60 min
hr := hour
day := 24 hr
d := day
da := day
week := 7 day
wk := week
sennight := 7 day
fortnight := 14 day
blink := 1ee-5 day // Actual human blink takes 1/3 second
ce := 1ee-2 day
//
// units derived easily from SI units
//
gm := gram
g := gram
tonne := 1000 kg
t := tonne
metricton := tonne
sthene := tonne m / s^2
funal := sthene
pieze := sthene / m^2
quintal := 100 kg
bar := 1ee5 Pa // About 1 atm
vac := millibar
micron := micrometer// One millionth of a meter
bicron := picometer // One brbillionth of a meter
cc := cm^3
are := 100 m^2
liter := 1000 cc // The liter was defined in 1901 as the
oldliter := 1.000028 dm^3// space occupied by 1 kg of pure water at
l := liter // the temperature of its maximum density
// under a pressure of 1 atm. This was
// supposed to be 1000 cubic cm, but it
// was discovered that the original
// measurement was off. In 1964, the
// liter was redefined to be exactly 1000
// cubic centimeters.
L := liter // This unit and its symbol l were adopted by
// the CIPM in 1879. The alternative symbol for
// the liter, L, was adopted by the CGPM in 1979
// in order to avoid the risk of confusion
// between the letter l and the number 1. Thus,
// although both l and L are internationally
// accepted symbols for the liter, to avoid this
// risk the preferred symbol for use in the
// United States is L.
mho := siemens // Inverse of ohm, hence ohm spelled backward
galvat := ampere // Named after Luigi Galvani
angstrom := 1ee-10 m // Convenient for describing molecular sizes
\u212b := angstrom // Official Unicode codepoint for
// Angstrom symbol: ANGSTROM SIGN
\u00c5 := angstrom // "Preferred" Unicode codepoint for
// Angstrom symbol:
// LATIN CAPITAL LETTER A WITH RING ABOVE
xunit := 1.00202e-13 meter// Used for measuring wavelengths
siegbahn := xunit // of X-rays. It is defined to be
// 1/3029.45 of the spacing of calcite
// planes at 18 degC. It was intended
// to be exactly 1e-13 m, but was
// later found to be off slightly.
fermi := 1ee-15 m // Convenient for describing nuclear sizes
// Nuclear radius is from 1 to 10 fermis
barn := 1ee-28 m^2 // Used to measure cross section for
// particle physics collision, said to
// have originated in the phrase "big as
// a barn".
shed := 1ee-24 barn// Defined to be a smaller companion to the
// barn, but it's too small to be of
// much use.
brewster := micron^2/N // measures stress-optical coef
diopter := m^-1 // measures reciprocal of lens focal length
fresnel := 1ee12 Hz // occasionally used in spectroscopy
shake := 1ee-8 sec
svedberg := 1ee-13 s // Used for measuring the sedimentation
// coefficient for centrifuging.
gamma := microgram
lambda := microliter
spat := 1ee12 m // Rarely used for astronomical measurements
preece := 1ee13 ohm m// resistivity
planck := J s // action of one joule over one second
sturgeon := henry^-1 // magnetic reluctance
sturgeon ||| magnetic_reluctance
daraf := 1/farad // elastance (farad spelled backwards)
leo := 10 m/s^2
poiseuille := N s / m^2 // viscosity
mayer := J/(g K) // specific heat capacity
mired := microK^-1 // reciprocal color temperature. The name
// abbreviates micro reciprocal degree.
crocodile := megavolt // used informally in UK physics labs
metricounce := 25 g
mounce := metricounce
finsenunit := 1ee5 W/m^2 // Measures intensity of ultraviolet light
// with wavelength 296.7 nm.
fluxunit := 1ee-26 W/(m^2 Hz)// Used in radio astronomy to measure
// the energy incident on the receiving
// body across a specified frequency
// bandwidth. [12]
jansky := fluxunit // K. G. Jansky identified radio waves coming
Jy := jansky // from outer space in 1931.
// Basic constants
pi := 3.141592653589793238
\u03c0 := pi // Unicode character for pi
// as a mathematical constant
// GREEK SMALL LETTER PI
e := 2.71828182845904523536 // Base of natural logarithm
// 'e' was previously used to be
// the charge of the electron, but
// changed to this. Mathematicians and
// particle physicists may battle this
// out.
c := 299792458 m/s // speed of light in vacuum (exact)
light := c
lightspeed := c // sure, why not.
mu0 := 4 pi 1e-7 H/m // permeability of vacuum (exact)
mu0 ||| permeability
epsilon0 := 1/(mu0 c^2) // permittivity of vacuum (exact)
// This is equivalent to about
// 8.85e-12 farads/meter
epsilon0 ||| permittivity
energy := c^2 // convert mass to energy
electroncharge := 1.602176462e-19 C // electron charge, also called e
// but that's reserved for the
// base of the natural logarithm
h := 6.62606876e-34 J s // Planck's constant
plancksconstant := h
\u210e := h // Official Unicode char for Planck's const.
hbar := h / (2 pi)
\u210f := hbar // Official Unicode char for Planck/2 pi
G := 6.673e-11 N m^2 / kg^2 // Newtonian gravity const
coulombconst := 1/(4 pi epsilon0) // listed as "k" sometimes
au := 1.49597870e11 m // astronomical unit, the average
// radius of earth's orbit around the
// sun, as defined by the IAU (1976)
ua := au // The SI defines this abbreviation as its preferred
// version
astronomicalunit := au
//
// angular measure
//
circle := 2 pi radian
degree := 1/360 circle
arcdegree := degree
deg := degree
arcdeg := arcdegree
arcminute := 1/60 degree
arcmin := arcminute
arcsecond := 1/60 arcmin
arcsec := arcsecond
mas := milliarcsecond
rightangle := 90 degrees
quadrant := 1/4 circle
quintant := 1/5 circle
sextant := 1/6 circle
sign := 1/12 circle// Angular extent of one sign of the zodiac
turn := circle
revolution := turn
rev := turn
pulsatance := radian / sec
gon := 1/100 rightangle // measure of grade
grade := gon
centesimalminute := 1/100 grade
centesimalsecond := 1/100 centesimalminute
milangle := 1/6400 circle // Official NIST definition.
// Another choice is 1ee-3 radian.
pointangle := 1/32 circle
centrad := 1/100 radian // Used for angular deviation of light
// through a prism.
brad := 1/256 circle // Binary radian--used to fit angular measurements into
// a byte. Questionable but what the hell.
//
// Solid angle measure
//
sphere := 4 pi sr
squaredegree := 1/180^2 pi^2 sr
squareminute := 1/60^2 squaredegree
squaresecond := 1/60^2 squareminute
squarearcmin := squareminute
squarearcsec := squaresecond
sphericalrightangle := 1/2 pi sr
octant := 1/2 pi sr
//
// Concentration measures
//
percent := 1/100
proof := 1/200 // Alcohol content measured by volume at
// 60 degrees Fahrenheit. This is a USA
// measure. In Europe proof=percent.
ppm := 1ee-6
partspermillion := ppm
ppb := 1ee-9
partsperbillion := ppb // USA billion
ppt := 1ee-12
partspertrillion := ppt // USA trillion
karat := 1/24 // measure of gold purity
fine := 1/1000 // Measure of gold purity
caratgold := karat
gammil := mg/l
basispoint := 1/100 percent// Used in finance
//
// Temperature difference
// The units below are NOT an absolute temperature measurement in Fahrenheit,
// but represents the size of a degree in the specified systems.
degcelsius := K
degreeCelsius := K // Per http://physics.nist.gov/Pubs/SP811/sec04.html#4.2.1.1
degC := K // The *size* of a degree in the Celsius scale.
// This is identical to the size of a Kelvin.
// WARNING: This should only be used when
// you're indicating the *difference* between
// two temperatures, (say, how much energy to
// raise the temperature of a gram of water by 5
// degrees Celsius, *not* for absolute
// temperatures. (I wonder if they should go
// entirely to eliminate this confusion...)
// For calculating absolute temperatures, use
// the Celsius[] or C[] functions below.
//
// In 1741 Anders Celsius introduced a
// Temperature scale with water boiling at 0
// degrees and freezing at 100 degrees at
// standard pressure. After his death the
// fixed points were reversed and the scale
// was called the centigrade scale. Due to
// the difficulty of accurately measuring the
// temperature of melting ice at standard
// pressure, the centigrade scale was replaced
// in 1954 by the Celsius scale which is
// defined by subtracting 273.15 from the
// temperature in Kelvins. This definition
// differed slightly from the old centigrade
// definition, but the Kelvin scale depends on
// the triple point of water rather than a
// melting point, so it can be measured
// accurately.
zerocelsius := 273.15 K // Defined by the 10th CGPM, 1954, Resolution 3;
// CR, 79. The triple point of water was defined
// at the same time to be 273.16 Kelvin, and
// the reference temperature 273.15 K (the ice
// point) to be the scale difference between
// Kelvin and Celsius. So, the size of a Kelvin
// and a degree Celsius are the same, but
// the zero point of the Celsius scale is actually
// set to .01 Kelvin below the triple point.
degfahrenheit := 5/9 degC // The *size* of a degree in the Fahrenheit scale.
degreeFahrenheit := degfahrenheit // The *size* of a degree in the Fahrenheit scale.
degF := degfahrenheit // WARNING: These should only be used when
// you're indicating the *difference* between
// two temperatures, (say, how much energy to
// raise the temperature of a gram of water by 5
// degrees Fahrenheit, *not* for absolute
// temperatures. (I wonder if they should go
// entirely to eliminate this confusion...)
// For calculating absolute temperatures, use
// the Fahrenheit[] or F[] functions below.
//
// Fahrenheit defined his temperature scale
// by setting 0 to the coldest temperature
// he could produce and by setting 96 degrees
// to body heat (for reasons unknown).
\u2109 := degfahrenheit // Single Unicode codepoint for
// DEGREE FAHRENHEIT
degreesRankine := 5/9 K
degreesrankine := degreesRankine // The Rankine scale has the
degrankine := degreesRankine // Fahrenheit degree, but its zero
degreerankine := degrankine // is at absolute zero.
degR := degrankine
Rankine := degreesrankine
degreaumur := 10/8 degC // The Reaumur scale was used in Europe and
// particularly in France. It is defined
// to be 0 at the freezing point of water
// and 80 at the boiling point. Reaumur
// apparently selected 80 because it is
// divisible by many numbers.
// Function for converting Fahrenheit to/from standard units
// This is a less legible version of the revised function below
//Fahrenheit[x] := (x conforms K) ? ((x - zerocelsius) / K) * 9/5 + 32 : ((x conforms 1) ? ((x-32) * 5/9) K + zerocelsius : "Error")
Fahrenheit[x] :=
{
if (x conforms K) // If x is already a temperature, convert to F
return ((x - zerocelsius) / K) * 9/5 + 32
else
if (x conforms 1) // If x is a pure number, treat as Fahrenheit degrees
return ((x-32) * 5/9) K + zerocelsius
else
return "Error"
}
// TODO: Change the implementation of the following idiom so that it aliases
// the function instead of chaining function calls.
F[x] := Fahrenheit[x]
// Function for converting Celsius to/from standard units
Celsius[x] := (x conforms K) ? (x-zerocelsius) / K : ((x conforms 1) ? (x K + zerocelsius) : "Error")
C[x] := Celsius[x]
Reaumur[x] := (x conforms K) ? (8/10 (x-zerocelsius)) / K : ((x conforms 1) ? (10/8 * x * K + zerocelsius) : "Error")
// Physical constants
//
gravity := 980665/100000 m/s^2 // std acceleration of gravity
// (exact)
g_n := gravity
gee := gravity
gravities := gravity // Irregular plural
force := gravity // use to turn masses into forces
// Various conventional values
atm := 101325 Pa // Standard atmospheric pressure (exact)
atmosphere := atm
Hg := 13.5951 gram / cm^3 // Density of mercury (defined)
mercurydensity := Hg
water := gram / cm^3 // Standard density of water (defined)
H2O := water
wc := water // water column
mach := 331.46 m/s // speed of sound in dry air at STP
standardtemp := 273.15 K // standard temperature
stdtemp := standardtemp
// Physico-chemical constants
atomicmassunit := 1.66053873e-27 kg // atomic mass unit (defined to be
u := atomicmassunit // 1/12 of the mass of carbon 12)
amu := atomicmassunit
amu_chem := 1.66026e-27 kg // 1/16 of the weighted average mass of
// the 3 naturally occuring neutral
// isotopes of oxygen
amu_phys := 1.65981e-27 kg // 1/16 of the mass of a neutral
// oxygen 16 atom
dalton := u // Maybe this should be amu_chem?
avogadro := grams/(amu mol) // size of a mole
N_A := avogadro
gasconstant := 8.314472 J / (mol K)// molar gas constant
R := gasconstant
boltzmann := R / N_A // Boltzmann's constant
boltzmannsconstant := boltzmann // Boltzmann's constant
k := boltzmann
molarvolume := mol R stdtemp / atm // Volume occupied by one mole of an
// ideal gas at STP.
molar := mol / l // Unit of concentration (moles/liter)
Molar := molar // Sometimes capitalized
molar ||| concentration_by_volume
molal := mol / kg // Unit of concentration (moles/kg)
molal ||| concentration_by_mass
m^3/mol ||| molar_volume
loschmidt := avogadro mol / molarvolume// Molecules per cubic meter of an
// ideal gas at STP. Loschmidt did
// work similar to Avogadro.
stefanboltzmann := 2 pi^5 k^4 / (15 h^3 c^2) // The radiant emittance by a
// blackbody
sigma := stefanboltzmann // at temperature T is given by
// sigma T^4.
wiendisplacement := 2.8977686e-3 m K // Wien's Displacement Law gives the
// frequency at which the the Planck
// spectrum has maximum intensity.
// The relation is lambda T = b where
// lambda is wavelength, T is
// temperature and b is the Wien
// displacement. This relation is
// used to determine the temperature
// of stars.
K_J := 2 electroncharge/h // Josephson Constant
// Direct measurement of the volt is difficult. Until
// recently, laboratories kept Weston cadmium cells as
// a reference, but they could drift. In 1987 the
// CGPM officially recommended the use of the
// Josephson effect as a laboratory representation of
// the volt. The Josephson effect occurs when two
// superconductors are separated by a thin insulating
// layer. A "supercurrent" flows across the insulator
// with a frequency that depends on the potential
// applied across the superconductors. This frequency
// can be very accurately measured. The Josephson
// constant K_J, which is equal to 2e/h, relates the
// measured frequency to the potential. The value
// given here is the officially specified value for
// use beginning in 1990. The 1998 recommended value
// of the constant is 483597.898 GHz/V.
R_K := h/electroncharge^2
// Measurement of the ohm also presents difficulties.
// The old approach involved maintaining resistances
// that were subject to drift. The new standard is
// based on the Hall effect. When a current carrying
// ribbon is placed in a magnetic field, a potential
// difference develops across the ribbon. The ratio
// of the potential difference to the current is
// called the Hall resistance. Klaus von Klitzing
// discovered in 1980 that the Hall resistance varies
// in discrete jumps when the magnetic field is very
// large and the temperature very low. This enables
// accurate realization of the resistance h/e^2 in the
// lab. This is approximately equal to 25812.807 ohms
// Density of mercury and water at different temperatures using the standard
// force of gravity.
// Hg10C := 13.5708 gram / cm^3 // These units, when used to form
// Hg20C := 13.5462 gram / cm^3 // pressure measures, are not accurate
// Hg23C := 13.5386 gram / cm^3 // because of considerations of the
// Hg30C := 13.5217 gram / cm^3 // revised practical temperature scale.
// Hg40C := 13.4973 gram / cm^3
// Hg60F := 13.5574 gram / cm^3
// H2O0C := 0.99987 gram / cm^3
// H2O5C := 0.99999 gram / cm^3
// H2O10C := 0.99973 gram / cm^3
// H2O15C := 0.99913 gram / cm^3
// H2O18C := 0.99862 gram / cm^3
// H2O20C := 0.99823 gram / cm^3
// H2O25C := 0.99707 gram / cm^3
// H2O50C := 0.98807 gram / cm^3
// H2O100C := 0.95838 gram / cm^3
// Masses of elementary particles
electronmass := 5.485799110e-4 u
m_e := electronmass
protonmass := 1.00727646688 u
m_p := protonmass
neutronmass := 1.00866491578 u
m_n := neutronmass
muonmass := 0.1134289168 u
m_mu := muonmass
deuteronmass := 2.01355321271 u
m_d := deuteronmass
alphaparticlemass := 4.0015061747 u
m_alpha := alphaparticlemass
muonmass := 0.1134289168 u
m_muon := muonmass
taumass := 1.90774 u
m_tau := taumass
// Atomic constants
alpha := mu0 c electroncharge^2 / (2 h)
// The fine structure constant was
// introduced to explain fine
// structure visible in spectral
// lines.
Rinfinity := m_e c alpha^2 / (2 h)
// The wavelengths of a spectral series
R_H := 10967760 /m // can be expressed as
// 1/lambda = R (1/m^2 - 1/n^2).
// where R is a number that various
// slightly from element to element.
// For hydrogen, R_H is the value,
// and for heavy elements, the value
// approaches Rinfinity.
bohrradius := alpha / (4 pi Rinfinity)
// Planck constants
planckmass := (hbar c / G)^(1/2)
m_P := planckmass
plancktime := hbar / (planckmass c^2)
t_P := plancktime
plancklength := plancktime c
l_P := plancklength
// particle wavelengths: the compton wavelength of a particle is
// defined as h / m c where m is the mass of the particle.
electronwavelength := h / (m_e c)
lambda_C := electronwavelength
protonwavelength := h / (m_p c)
lambda_C_p := protonwavelength
neutronwavelength := h / (m_n c)
lambda_C_n := neutronwavelength
// Magnetic moments
bohrmagneton := electroncharge hbar / (2 electronmass)
mu_B := bohrmagneton
nuclearmagneton := electroncharge hbar / (2 protonmass)
mu_N := nuclearmagneton
mu_mu := 4.49044813e-26 J/T // Muon magnetic moment
mu_p := 1.410606633e-26 J/T// Proton magnetic moment
mu_e := 928.476362e-26 J/T // Electron magnetic moment
mu_n := 0.96623640e-26 J/T // Neutron magnetic moment
mu_d := 0.433073457e-26 J/T// Deuteron magnetic moment
//
// United States units
//
// linear measure
// The US Metric Law of 1866 gave the exact relation 1 meter = 39.37 inches.
// From 1893 until 1959, the foot was exactly 1200/3937 meters. In 1959
// the definition was changed to bring the US into agreement with other
// countries. Since then, the foot has been exactly 0.3048 meters. At the
// same time it was decided that any data expressed in feet derived from
// geodetic surveys within the US would continue to use the old definition.
inch := 254/100 cm
foot := 12 inch
feet := foot
ft := foot
survey ::- 1200/3937 m/ft // Ratio to give survey length
geodetic ::- survey
statute ::- survey
int :- 3937/1200 ft/m // Convert US Survey measures to
// international measures
inches := inch // Wacky plural
in := inch
yard := 3 ft
yd := yard
mile := 5280 ft
line := 1/12 inch // Also defined as '.1 in' or as '1e-8 Wb'
rod := 11/2 surveyyard
rd := rod
perch := rod
furlong := 40 rod // From "furrow long"
statutemile := statute mile
league := 3 statute mile
// Calories: energy to raise a gram of water one degree celsius
cal_IT := 41868/10000 J // International Table calorie
cal_th := 4184/1000 J // Thermochemical calorie
cal_fifteen := 4.18580 J // Energy to go from 14.5 to 15.5 degC
cal_twenty := 4.18190 J // Energy to go from 19.5 to 20.5 degC
cal_mean := 4.19002 J // 1/100 energy to go from 0 to 100 degC
calorie := cal_IT
cal := calorie
calorie_IT := cal_IT
thermcalorie := cal_th
calorie_th := thermcalorie
Calorie := kilocalorie // the food Calorie
thermie := 1ee6 cal_fifteen// Heat required to raise the
// temperature of a tonne of
// water from 14.5 to 15.5 degC.
//
// Units derived from physical constants
//
inHg := inch gravity Hg // Inches of mercury
inH2O := inch gravity water
inchmercury := inHg
inchesmercury := inHg // Irregular plural
mmH2O := mm gravity water
mmHg := mm gravity Hg
kgf := kg gravity
technicalatmosphere := kgf / cm^2
at := technicalatmosphere
hyl := kgf s^2 / m // Also gram-force s^2/m according to [15]
torr := 101325/760 Pa // Exactly defined. Differs from mmHg by
// about 1 part in 7 million.
Torr := torr // Accepted symbol is Torr
// These units, both named after Evangelista
tor := Pa // Torricelli, should not be confused.
// Acording to [15] the torr is actually
// atm/760 which is slightly different.
eV := electroncharge V // Energy acquired by a particle with charge e
electronvolt := eV // when it is accelerated through 1 V
lightyear := c 365.25 day // The 365.25 day year is specified in
// NIST publication 811
ly := lightyear
lightsecond := c s
lightminute := c min
parsec := au radian / arcsec // Unit of length equal to distance
pc := parsec // from the sun to a point having
// heliocentric parallax of 1
// arcsec (derived from parallax
// second) The formula should use
// tangent, but the error is about
// 1e-12.
rydberg := h c Rinfinity // Rydberg energy
crith := 0.089885 gram // The crith is the mass of one
// liter of hydrogen at standard
// temperature and pressure.
amagatvolume := molarvolume
amagat := mol/amagatvolume // Used to measure gas densities
lorentz := bohrmagneton / (h c)// Used to measure the extent
// that the frequency of light
// is shifted by a magnetic field.
cminv := h c / cm // Unit of energy used in infrared
invcm := cminv // spectroscopy.
wavenumber := cminv
kcal_mol := kcal / (mol N_A) // kcal/mol is used as a unit of
// energy by physical chemists.
//
// CGS system based on centimeter, gram and second
//
dyne := cm gram / s^2 // force
dyn := dyne
erg := cm dyne // energy
poise := gram / (cm s) // viscosity, honors Jean Poiseuille
P := poise
poise ||| viscosity
rhe := poise^-1 // reciprocal viscosity
rhe ||| reciprocal_viscosity
stokes := cm^2 / s // kinematic viscosity
St := stokes
stokes ||| kinematic_viscosity
stoke := stokes
lentor := stokes // old name
Gal := cm / s^2 // acceleration, used in geophysics
galileo := Gal // for earth's gravitational field
// (note that "gal" is for gallon
// but "Gal" is the standard symbol
// for the gal which is evidently a
// shortened form of "galileo".)
barye := dyne/cm^2 // pressure
barad := barye // old name
kayser := 1/cm // Proposed as a unit for wavenumber
balmer := kayser // Even less common name than "kayser"
kine := cm/s // velocity
bole := g cm / s // momentum
pond := gram force
glug := gram force s^2 / cm// Mass which is accelerated at
// 1 cm/s^2 by 1 gram force
darcy := centipoise cm^2 /(s atm)// Measures permeability to fluid flow.
// One darcy is the permeability of a
// medium that allows a flow of cc/s of
// a liquid of centipoise viscosity
// under a pressure gradient of atm/cm.
mohm := cm / (dyn s) // mobile ohm, measure of mechanical
mobileohm := mohm // mobility
mechanicalohm := dyn s / cm // mechanical resistance
acousticalohm := dyn s / cm^5 // ratio of the sound pressure of
// 1 dyn/cm^2 to a source of strength
// 1 cm^3/s
ray := acousticalohm
rayl := dyn s / cm^3 // Specific acoustical resistance
eotvos := 1ee-9 Gal/cm // Change in gravitational acceleration
// over horizontal distance
// Electromagnetic units derived from the abampere
abampere := 10 A // Current which produces a force of
abamp := abampere // 2 dyne/cm between two infinitely
aA := abampere // long wires that are 1 cm apart
biot := aA // alternative name for abamp
Bi := biot
abcoulomb := abamp sec
abcoul := abcoulomb
abvolt := dyne cm / (abamp sec)
abfarad := abampere sec / abvolt
abhenry := abvolt sec / abamp
abohm := abvolt / abamp
abmho := abohm^-1
gauss := abvolt sec / cm^2
Gs := gauss
maxwell := abvolt sec // Also called the "line"
Mx := maxwell
oersted := gauss / mu0
Oe := oersted
gilbert := gauss cm / mu0
Gb := gilbert
Gi := gilbert
unitpole := 4 pi maxwell
// Gaussian system: electromagnetic units derived from statampere.
//
// Note that the Gaussian units are often used in such a way that Coulomb's law
// has the form F= q1 * q2 / r^2. The constant 1/4*pi*epsilon0 is incorporated
// into the units. From this, we can get the relation force=charge^2/dist^2.
// This means that the simplification esu^2 = dyne cm^2 can be used to simplify
// units in the Gaussian system, with the curious result that capacitance can be
// measured in cm, resistance in sec/cm, and inductance in sec^2/cm. These
// units are given the names statfarad, statohm and stathenry below.
statampere := 10 A cm / (s c)
statamp := statampere
statvolt := dyne cm / (statamp sec)
statcoulomb := statamp s
esu := statcoulomb
statcoul := statcoulomb
statfarad := statamp sec / statvolt
cmcapacitance := statfarad
stathenry := statvolt sec / statamp
statohm := statvolt / statamp
statmho := statohm^-1
statmaxwell := statvolt sec
franklin := statcoulomb
debye := 1ee-18 statcoul cm// unit of electrical dipole moment
debye ||| electrical_dipole_moment
helmholtz := debye/angstrom^2 // Dipole moment per area
jar := 1000 statfarad // approx capacitance of Leyden jar
//
// Some historical eletromagnetic units
//
intampere := 0.999835 A // Defined as the current which in one
intamp := intampere // second deposits .001118 gram of
// silver from an aqueous solution of
// silver nitrate.
intfarad := 0.999505 F
intvolt := 1.00033 V
intohm := 1.000495 ohm // Defined as the resistance of a
// uniform column of mercury containing
// 14.4521 gram in a column 1.063 m
// long and maintained at 0 degC.
daniell := 1.042 V // Meant to be electromotive force of a
// Daniell cell, but in error by .04 V
faraday := N_A electroncharge mol // Charge that must flow to deposit or
faraday_phys := 96521.9 C // liberate one gram equivalent of any
faraday_chem := 96495.7 C // element. (The chemical and physical
// values are off slightly from what is
// obtained by multiplying by amu_chem
// or amu_phys. These values are from
// a 1991 NIST publication.) Note that
// there is a Faraday constant which is
// equal to N_A e and hence has units of
// C/mol.
kappline := 6000 maxwell // Named by and for Gisbert Kapp
siemensunit := 0.9534 ohm // Resistance of a meter long column of
// mercury with a 1 mm cross section.
//
// Photometric units
//
candle := 1.02 candela // Standard unit for luminous intensity
hefnerunit := 0.9 candle // in use before candela
hefnercandle := hefnerunit //
violle := 20.17 cd // luminous intensity of 1 cm^2 of
// platinum at its temperature of
// solidification (2045 K)
lumen := cd sr // Luminous flux
lm := lumen //
talbot := lumen s // Luminous energy
lumberg := talbot
talbot ||| luminous_energy
m^-2 cd sr ||| illuminance
lux := lm/m^2 // Illuminance or exitance (luminous
lx := lux // flux incident on or coming from
phot := lumen / cm^2 // a surface)
ph := phot //
footcandle := lumen/ft^2 // Illuminance from a 1 candela source
// at a distance of one foot
metercandle := lumen/m^2 // Illuminance from a 1 candela source
// at a distance of one meter
mcs := metercandle s// luminous energy per area, used to
// measure photographic exposure
// Luminance measures
nit := cd/m^2 // Luminance: the intensity per projected
stilb := cd / cm^2 // area of an extended luminous source.
sb := stilb // (nit is from latin nitere = to shine.)
apostilb := cd/(pi m^2)
asb := apostilb
blondel := apostilb // Named after a French scientist.
nox := 1ee-3 lux // These two units were proposed for
skot := 1ee-3 apostilb// measurements relating to dark adapted
// eyes.
// Equivalent luminance measures. These units are units which measure
// the luminance of a surface with a specified exitance which obeys
// Lambert's law. (Lambert's law specifies that luminous intensity of
// a perfectly diffuse luminous surface is proportional to the cosine
// of the angle at which you view the luminous surface.)
equivalentlux := cd / (pi m^2) // luminance of a 1 lux surface
equivalentphot := cd / (pi cm^2) // luminance of a 1 phot surface
lambert := cd / (pi cm^2)
footlambert := cd / (pi ft^2)
// Some luminance data from the IES Lighting Handbook, 8th ed, 1993
sunlum := 1.6e9 cd/m^2 // at zenith
sunillum := 100e3 lux // clear sky
sunillum_o := 10e3 lux // overcast sky
sunlum_h := 6e6 cd/m^2 // value at horizon
skylum := 8000 cd/m^2 // average, clear sky
skylum_o := 2000 cd/m^2 // average, overcast sky
moonlum := 2500 cd/m^2
//
// Astronomical time measurements
//
anomalisticyear := 365.2596 days // The time between successive
// perihelion passages of the
// earth.
siderealyear := 365.256360417 day // The time for the earth to make
// one revolution around the sun
// relative to the stars.
tropicalyear := 365.242198781 day // The mean interval between vernal
// equinoxes. Differs from the
// sidereal year by 1 part in
// 26000 due to precession of the
// earth about its rotational axis
// combined with precession of the
// perihelion of the earth's
// orbit.
gaussianyear := 365.2690 days // The orbital period of a body in
// circular orbit at a distance of
// 1 au from the sun. Calculated
// from Kepler's third law.
siderealday := 23.934469444 hour // The sidereal day is the interval
siderealhour := 1/24 siderealday // between two successive transits
siderealminute := 1/60 siderealhour // of a star over the meridian,
siderealsecond := 1/60 siderealminute// or the time required for the
// earth to make one rotation
// relative to the stars. The
// more usual solar day is the
// time required to make a
// rotation relative to the sun.
// Because the earth moves in its
// orbit, it has to turn a bit
// extra to face the sun again,
// hence the solar day is slightly
// longer.
anomalisticmonth := 27.55454977 day // Time from perigee to perigee
nodicalmonth := 27.2122199 day // The nodes are the points where
draconicmonth := nodicalmonth // an orbit crosses the ecliptic.
draconiticmonth := nodicalmonth // This is the time required to
// travel from the ascending node
// to the next ascending node.
siderealmonth := 27.321661 day // Time required for the moon to
// orbit the earth
lunarmonth := 29.5305555 day // Time between full moons. Full
synodicmonth := lunarmonth // moon occur when the sun and
lunation := synodicmonth // moon are on opposite sides of
lune := 1/30 lunation // the earth. Since the earth
lunour := 1/24 lune // moves around the sun, the moon
// has to revolve a bit farther to
// get into the full moon
// configuration.
year := tropicalyear
yr := year
month := 1/12 year // This is obviously an average for the
// limiting case... so is accurate in the
// long term but useless for adding an
// offset to a specific date.
mo := month
decade := 10 years
century := 100 years
centuries := century // Irregular plural
millennium := 1000 years
millennia := millennium
solaryear := year
lunaryear := 12 lunarmonth
calendaryear := 365 day
commonyear := 365 day
leapyear := 366 day
julianyear := 365.25 day
juliancentury := 36525 day
juliancenturies := 36525 day
gregorianyear := 365.2425 day
islamicyear := 354 day // A year of 12 lunar months. They
islamicleapyear := 355 day // began counting on July 16, AD 622
// when Muhammad emigrated to Medina
// (the year of the Hegira). They need
// 11 leap days in 30 years to stay in
// sync with the lunar year which is a
// bit longer than the 29.5 days of the
// average month.
islamicmonth := 1/12 islamicyear// They have 29 day and 30 day months.
cron := 1ee6 years
lustrum := 5 years // The Lustrum was a Roman
// purification ceremony that took
// place every five years.
// Classically educated Englishmen
// used this term.
// Sidereal days
mercuryday := 58.6462 day
venusday := 243.01 day // retrograde
earthday := siderealday
marsday := 1.02595675 day
jupiterday := 0.41354 day
saturnday := 0.4375 day
uranusday := 0.65 day // retrograde
neptuneday := 0.768 day
plutoday := 6.3867 day
// Planetary sidereal years
mercuryyear := 86.96 day
venusyear := 224.68 day
earthyear := siderealyear
marsyear := 686.95 day
jupiteryear := 11.862 tropicalyear
saturnyear := 29.458 tropicalyear
uranusyear := 84.012 tropicalyear
neptuneyear := 164.798 tropicalyear
plutoyear := 248.5 tropicalyear
//
// Some other astronomical values
//
sunmass := 1.9891e30 kg
sunradius := 6.96e8 m
sunpower := 3.86e26 watts
landarea := 148.847e6 km^2
oceanarea := 361.254e6 km^2
moonmass := 7.3483e22 kg
moonradius := 1738 km // mean value
// Distances
sundist := 1.0000010178 au// mean earth-sun distance
sundist_near := 1.471e11 m // earth-sun distance at perihelion
sundist_far := 1.521e11 m // earth-sun distance at aphelion
// Average distances between planets and the sun.
mercurydist := 57910. Mm
venusdist := 108200. Mm
earthdist := sundist
marsdist := 227940. Mm
jupiterdist := 778330. Mm
saturndist := 1429400. Mm
uranusdist := 2870990. Mm
neptunedist := 4497070. Mm
plutodist := 5913520. Mm
moondist := 384400. km // mean earth-moon distance
mercurymass := 0.33022e24 kg
venusmass := 4.8690e24 kg
marsmass := 0.64191e24 kg
earthmass := 5.9742e24 kg
jupitermass := 1898.8e24 kg
saturnmass := 568.5e24 kg
uranusmass := 86.625e24 kg
neptunemass := 102.78e24 kg
plutomass := 0.0127e24 kg
mercuryradius := 2439. km
venusradius := 6052. km
marsradius := 3397. km
earthradius := 6371.01 km // mean +/- 0.02 km
jupiterradius := 71492. km
saturnradius := 60268. km
uranusradius := 25559. km
neptuneradius := 24764. km
plutoradius := 1137. km
earthradius_polar := 6356.755 km
earthradius_equatorial := 6378.140 km
// Larger moons... their distances are the average distances from their planet.
// Jupiter
iodist := 422000. km
ioradius := 1815. km
iomass := 8.93e22 kg
europadist := 670900. km
europaradius := 1569. km
europamass := 4.80e22 kg
ganymededist := 1070000. km
ganymederadius := 2631. km
ganymedemass := 1.48e23 kg
callistodist := 1883000. km
callistoradius := 2400. km
callistomass := 1.08e23 kg
// Pluto
charondist := 19640. km
charonradius := 586. km
charonmass := 1.90e21 kg
moongravity := 1.62 m/s^2
atomicmass := electronmass
atomiccharge := electroncharge
atomicaction := hbar
// Inverse time units
annually := 1/year
annual := annually
yearly := annual
daily := 1/day
weekly := 1/week
monthly := 1/month
hourly := 1/hour
// Perfect intervals
octave := 2
majorthird := 5/4
minorthird := 6/5
musicalfourth := 4/3
musicalfifth := 3/2
majorsecond := musicalfifth^2 / octave
majorsixth := musicalfourth majorthird
minorsixth := musicalfourth minorthird
majorseventh := musicalfifth majorthird
minorseventh := musicalfifth minorthird
pythagoreanthird := majorsecond musicalfifth^2 / octave
syntoniccomma := pythagoreanthird / majorthird
pythagoreancomma := musicalfifth^12 / octave^7
// Equal tempered definitions
semitone := octave^(1/12)
//
// The Hartree system of atomic units, derived from fundamental units
// of mass (of electron), action (planck's constant), charge, and
// the coulomb constant.
// Fundamental units
// derived units (Warning: accuracy is lost from deriving them this way)
atomiclength := bohrradius
atomictime := hbar^3/(coulombconst^2 atomicmass electroncharge^4)
// Period of first Bohr orbit
atomicvelocity := atomiclength / atomictime
atomicenergy := hbar / atomictime
hartree := atomicenergy
Hartree := hartree
//
// These thermal units treat entropy as charge, from [5]
//
thermalcoulomb := J/K // entropy
thermalampere := W/K // entropy flow
thermalfarad := J/K^2
thermalohm := K^2/W // thermal resistance
fourier := thermalohm
thermalhenry := J K^2/W^2 // thermal inductance
thermalvolt := K // thermal potential difference
// surveyor's measure
surveyorschain := 66 surveyft
surveyorspole := 1/4 surveyorschain
surveyorslink := 1/100 surveyorschain
chain := surveyorschain
surveychain := chain
ch := chain
link := surveyorslink
acre := 43560 surveyfoot^2 // NIST Handbook 44 has a
// typographical error (forgetting
// to underline feet in one place
// on middle of page C-16 in 2003
// edition) with
// respect to this, but it's
// clear from corroborating
// different figures in that
// document and NIST Special
// Publication 811, Sec. B.6,
// that the survey foot is
// the proper definition. Have
// filed errata with NIST and
// requested confirmation.
// 2003-08-27
intacre := 43560 ft^2 // Acre based on international ft
acrefoot := acre surveyfoot
acrefeet := acrefoot // Irregular plural
section := surveymile^2
township := 36 section
homestead := 160 acre // Area of land granted by the 1862 Homestead
// Act of the United States Congress
gunterschain := surveyorschain
engineerschain := 100 ft
engineerslink := 1/100 engineerschain
ramsdenschain := engineerschain
ramsdenslink := engineerslink
// nautical measure
fathom := 6 surveyft // Originally defined as the distance from
// fingertip to fingertip with arms fully
// extended.
nauticalmile := 1852 m // Supposed to be one minute of latitude at
// the equator. That value is about 1855 m.
// Early estimates of the earth's circumference
// were a bit off. The value of 1852 m was
// made the international standard in 1929.
// The US did not accept this value until
// July 1, 1954. The UK switched in 1970.
// The value of this unit was adopted by the
// First International Extraordinary
// Hydrographic Conference, Monaco, 1929,
// under the name "International nautical mile."
oldUSnauticalmile := 6080.20 feet // Used in U.S. before July 1, 1954
oldUSknot := oldUSnauticalmile / hour
cable := 720 surveyfoot // NIST Handbook 44, 2003 Appendix C
cablelength := cable
cableslength := cable
metriccable := 200 m // Used by France and Spain
navycablelength := 720 surveyft
marineleague := 3 nauticalmile
knot := nauticalmile / hr
shackle := 15 fathoms // Adopted 1949 by British navy
oldUKRNshackle := 12.5 fathoms // Used by Royal Navy until 1949
watch := 4 hours // time a sentry stands watch or a ship's
// crew is on duty.
bell := 1/8 watch // Bell would be sounded every 30 minutes.
// Avoirdupois weight
// These are actually defined as mass units to follow the recommendations
// of the SI.
pound := 45359237/100000000 kg // Defined exactly
lb := pound // From the latin libra
grain := 1/7000 pound // The grain is the same in all three
// weight systems. It was originally
// defined as the weight of a barley
// corn taken from the middle of the
// ear.
gr := grain
ounce := 1/16 pound
oz := ounce
dram := 1/16 ounce
dr := dram
hundredweight := 100 pounds // This is the USA hundredweight
cwt := hundredweight
shorthundredweight := hundredweight
ton := 2000 lb
shortton := ton
shortquarter := 1/4 shortton
// Troy Weight. In 1828 the troy pound was made the first United States
// standard weight. It was to be used to regulate coinage.
troypound := 5760 grain
troyounce := 1/12 troypound
ozt := troyounce
pennyweight := 1/20 troyounce // Abbreviated "d" in reference to a
dwt := pennyweight // Frankish coin called the "denier"
// minted in the late 700's. There
// were 240 deniers to the pound.
assayton := mg ton / troyounce // mg / assayton = troyounce / ton
// Some other jewelers units
metriccarat := 2/10 gram
metricgrain := 50 mg
carat := metriccarat
ct := carat
jewelerspoint := 1/100 carat
silversmithpoint := 1/4000 inch
// Apothecaries' weight
appound := troypound
apounce := troyounce
apdram := 1/8 apounce
scruple := 1/3 apdram
// Liquid measure
gallon := 231 in^3
gal := gallon
quart := 1/4 gallon
qt := quart
pint := 1/2 qt
pt := pint
gill := 1/4 pint
fluidounce := 1/16 pint
floz := fluidounce
fluiddram := 1/8 floz
fldr := fluiddram
minim := 1/60 fldr
liquidbarrel := 31.5 gallon
petroleumbarrel := 42 gallon // Originated in Pennsylvania oil
// fields, from the winetierce
barrel := petroleumbarrel
oilbarrel := petroleumbarrel
bbl := barrel
hogshead := 63 gallon
firkin := 9 gallon
// Dry measures: The Winchester Bushel was defined by William III in 1702 and
// legally adopted in the US in 1836.
drybarrel := 7056 in^3
bushel := 2150.42 in^3 // Volume of 8 inch cylinder with 18.5
bu := bushel // inch diameter (rounded)
peck := 1/4 bushel
pk := peck
drygallon := 1/2 peck
dryquart := 1/4 drygallon
drypint := 1/2 dryquart
// Grain measures. The bushel as it is used by farmers in the USA is actually
// a measure of mass which varies for different commodities. Canada uses the
// same bushel masses for most commodities, but not for oats.
wheatbushel := 60 lb
soybeanbushel := 60 lb
cornbushel := 56 lb
ryebushel := 56 lb
barleybushel := 48 lb
oatbushel := 32 lb
ricebushel := 45 lb
canada_oatbushel := 34 lb
// Wine and Spirits measure
pony := 1 floz
jigger := 1.5 floz // Can vary between 1 and 2 floz
shot := jigger // Sometimes 1 floz
eushot := 25 ml // EU standard spirits measure
fifth := 1/5 gallon
winebottle := 750 ml // US industry standard, 1979
winesplit := 1/4 winebottle
wineglass := 4 floz
magnum := 1.5 liter // Standardized in 1979, but given
// as 2 qt in some references
metrictenth := 375 ml
metricfifth := 750 ml
metricquart := 1 liter
// French champagne bottle sizes
split := 200 ml
jeroboam := 2 magnum
rehoboam := 3 magnum
methuselah := 4 magnum
salmanazar := 6 magnum
balthazar := 8 magnum
nebuchadnezzar := 10 magnum
// Shoe measures
shoeiron := 1/48 inch // Used to measure leather in soles
shoeounce := 1/64 inch // Used to measure non-sole shoe leather
//
// USA slang units
//
buck := dollar
fin := 5 dollar
sawbuck := 10 dollar
key := kg // usually of marijuana, 60's
lid := 1 oz // Another 60's weed unit
footballfield := 100 yards
marathon := 26 miles + 385 yards
//
// British
//
british :- 1200000/3937014 m/ft // The UK lengths were defined by
// a bronze bar manufactured in
// 1844. Measurement of that bar
// revealed the dimensions given
// here.
// Old nautical definitions
// See: http://www.hemyockcastle.co.uk/nautical.htm
oldbrnauticalmile := 6080 ft // Used until 1970 when the UK
oldbrknot := oldbrnauticalmile / hr // switched to the international
oldbrcable := 1/10 oldbrnauticalmile // nautical mile.
geographicalmile := oldbrnauticalmile
admiraltymile := oldbrnauticalmile
admiraltyknot := oldbrknot
admiraltycable := oldbrcable
seamile := 6000 ft
cablet := 120 fathoms
hawserlaidcable := 130 fathoms
oldrussiancable := 100 fathoms
oldhollandcable :- 123 fathoms
oldportugalcable:= 141 fathoms
// British Imperial weight is mostly the same as US weight. A few extra
// units are added here.
clove := 7 lb
stone := 14 lb
brhundredweight := 8 stone
brquartermass := 1/4 brhundredweight
longhundredweight := brhundredweight
longton := 20 brhundredweight
brton := longton
brassayton := mg brton / troyounce
// British Imperial volume measures
brgallon := 454609/100000 l // The British Imperial gallon was
canadiangallon := brgallon // defined in 1824 to be the volume of
cangallon := brgallon // water which weighed 10 pounds at 62
// deg F with a pressure of 30 inHg.
// In 1963 it was defined to be the space
// occupied by 10 pounds of distilled
// water of density 0.998859 g/ml weighed
// in air of density 0.001217 g/ml
// against weights of density 8.136 g/ml.
// The value given here is given by [1]
// as an exact value.
imperialgallon := brgallon
brquart := 1/4 brgallon
imperialquart := brquart
brpint := 1/2 brquart
imperialpint := brpint
brfloz := 1/20 brpint // Note difference in definition
imperialfloz := brfloz
brdram := 1/8 brfloz
imperialdram := brdram
brminim := 1/60 brdram
imperialminim := brminim
brscruple := 1/3 brdram
imperialscruple := brscruple
fluidscruple := brscruple
brfluidounce := brfloz
imperialfluidounce := brfloz
brgill := 1/4 brpint
imperialgill := brgill
brpeck := 2 brgallon
imperialpeck := brpeck
brbarrel := 36 brgallon // Used for beer
imperialbarrel := brbarrel
brbushel := 4 brpeck
imperialbushel := brbushel
brheapedbushel := 1.278 brbushel
brquarter := 8 brbushel
brchaldron := 36 brbushel
// Obscure British volume measures. These units are generally traditional
// measures whose definitions have fluctuated over the years. Often they
// depended on the quantity being measured. They are given here in terms of
// British Imperial measures. For example, the puncheon may have historically
// been defined relative to the wine gallon or beer gallon or ale gallon
// rather than the British Imperial gallon.
bag := 4 brbushel
bucket := 4 brgallon
last := 40 brbushel
noggin := brgill
pottle := 1/2 brgallon
pin := 4.5 brgallon
puncheon := 72 brgallon
seam := 8 brbushel
coomb := 4 brbushel
boll := 6 brbushel
firlot := 1/4 boll
brfirkin := 9 brgallon // Used for ale and beer
cran := 37.5 brgallon // measures herring, about 750 fish
barrelbulk := 5 feet^3
brhogshead := 63 brgallon
registerton := 100 ft^3 // Used for internal capacity of ships
shippington := 40 ft^3 // Used for ship's cargo freight or timber
brshippington := 42 ft^3 //
freightton := shippington// Both register ton and shipping ton derive
// from the "tun cask" of wine.
displacementton := 35 ft^3 // Approximate volume of a longton weight of
// sea water used to measure ship displacement
waterton := 224 brgallon
strike := 70.5 l // 16th century unit, sometimes
// defined as .5, 2, or 4 bushels
// depending on the location. It
// probably doesn't make a lot of
// sense to define in terms of imperial
// bushels. Zupko gives a value of
// 2 Winchester grain bushels or about
// 70.5 liters.
// obscure British lengths
barleycorn := 1/3 britishinch // Given in Realm of Measure as the
// difference between successive shoe sizes
nail := 1/16 britishyard // Originally the width of the thumbnail,
// or 1/16 ft. This took on the general
// meaning of 1/16 and settled on the
// nail of a yard or 1/16 yards as its
// final value. [12]
pole := 16.5 britishft
rope := 20 britishft
englishell := 45 britishinch
flemishell := 27 britishinch
ell := englishell // supposed to be measure from elbow to
// fingertips
span := 9 britishinch // supposed to be distance from thumb
// to pinky with full hand extension
goad := 4.5 britishft // used for cloth
// misc obscure British units
rood := 1/4 acre
englishcarat := 3.163 grain // Originally intended to be 4 grain
// but this value ended up being
// used in the London diamond market
mancus := 2 oz
mast := 2.5 lb
basebox := 31360 in^2 // Used in metal plating
// alternate spellings
metre := meter
gramme := gram
litre := liter
dioptre := diopter
//
// Units derived the human body (may not be very accurate)
//
geometricpace := 5 ft // distance between points where the same
// foot hits the ground
pace := 2.5 ft// distance between points where alternate
// feet touch the ground
USmilitarypace := 30 in // United States official military pace
USdoubletimepace := 36 in // United States official doubletime pace
fingerbreadth := 7/8 in// The finger is defined as either the width
fingerlength := 4.5 in// or length of the finger
finger := fingerbreadth
hand := 4 inch// width of hand
palmwidth := hand // The palm is a unit defined as either the width
palmlength := 8 in // or the length of the hand
//
// Cooking measures
//
// US measures
cup := 8 floz
tablespoon := 1/16 cup
tbl := tablespoon
tbsp := tablespoon
Tbsp := tablespoon
Tsp := tablespoon
teaspoon := 1/3 tablespoon
tsp := teaspoon
metriccup := 250 ml
// US can sizes.
number1can := 10 floz
number2can := 19 floz
number2_5can := 3.5 cups
number3can := 4 cups
number5can := 7 cups
number10can := 105 floz
// British measures
brcup := 1/2 brpint
brteacup := 1/3 brpint
brtablespoon := 15 ml // Also 5/8 brfloz, approx 17.7 ml
brteaspoon := 1/3 brtablespoon // Also 1/4 brtablespoon
dessertspoon := 2 brteaspoon
brtsp := brteaspoon
brtbl := brtablespoon
dsp := dessertspoon
// Australian
australiatablespoon := 20 ml
austbl := australiatablespoon
// Chinese
// Thai measurements are very similar so the name must be qualified
chinesecatty := 1/2 kg
oldchinesecatty := 4/3 lbs // Before metric conversion.
chinesetael := 1/16 oldchinesecatty
chinesemace := 1/10 chinesetael
oldchinesepicul := 100 oldchinesecatty
chinesepicul := 100 chinesecatty // Chinese usage
// Thai weights
thaitical := 15 grams
thaibaht := thaitical // New name for thaitical, not to be confused with
// the Thai currency called "Thailand_baht".
thaisalung := 1/4 thaitical
thaifung := 1/2 thaisalung
thaisatang := 1/100 thaitical
thaisadtahng := thaisatang // Alternate transliteration
thaitamlung := 4 thaitical
thaicatty := 10 thaitamlung
thaichang := 2 thaicatty
thaihap := 50 thaichang
thaipicul := thaihap
thaikoyan := 20 thaipicul
// Japanese
japancup := 200 ml
// densities of cooking ingredients from The Cake Bible by Rose Levy Beranbaum
// so you can convert '2 cups sugar' to grams, for example, or in the other
// direction grams could be converted to 'cup flour_scooped'.
butter := 8. oz/cup
butter_clarified := 6.8 oz/cup
cocoa_butter := 9. oz/cup
shortening := 6.75 oz/cup // vegetable shortening
stickbutter := 1/4 lb
vegetable_oil := 7.5 oz/cup
cakeflour_sifted := 3.5 oz/cup // The density of flour depends on the
cakeflour_spooned := 4. oz/cup // measuring method. "Scooped", or
cakeflour_scooped := 4.5 oz/cup // "dip and sweep" refers to dipping a
flour_sifted := 4. oz/cup // measure into a bin, and then sweeping
flour_spooned := 4.25 oz/cup // the excess off the top. "Spooned"
flour_scooped := 5. oz/cup // means to lightly spoon into a measure
breadflour_sifted := 4.25 oz/cup // and then sweep the top. Sifted means
breadflour_spooned := 4.5 oz/cup // sifting the flour directly into a
breadflour_scooped := 5.5 oz/cup // measure and then sweeping the top.
cornstarch := 120. grams/cup
dutchcocoa_sifted := 75. g/cup // These are for Dutch processed cocoa
dutchcocoa_spooned := 92. g/cup
dutchcocoa_scooped := 95. g/cup
cocoa_sifted := 75. g/cup // These are for nonalkalized cocoa
cocoa_spooned := 82. g/cup
cocoa_scooped := 95. g/cup
heavycream := 232. g/cup
milk := 242. g/cup
sourcream := 242. g/cup
molasses := 11.25 oz/cup
cornsyrup := 11.5 oz/cup
honey := 11.75 oz/cup
sugar := 200. g/cup
powdered_sugar := 4. oz/cup
brownsugar_light := 217. g/cup // packed
brownsugar_dark := 239. g/cup
baking_powder := 4.6 grams / tsp
salt := 6 g / tsp
koshersalt := 2.8 g / tsp // Diamond Crystal salt, from package
// Note that Morton kosher salt is
// much denser.
ethanol := .7893 g/cm^3 // Density of ethanol
alcohol := ethanol // For now, density of ethanol
// Egg weights and volumes for a USA large egg
egg := 50. grams
eggwhite := 30. grams
eggyolk := 18.6 grams
eggvolume := 3. tablespoons + 1/2 tsp
eggwhitevolume := 2. tablespoons
eggyolkvolume := 3.5 tsp
//
// Units derived from imperial system
//
ouncedal := oz ft / s^2 // force which accelerates an ounce
// at 1 ft/s^2
poundal := lb ft / s^2 // same thing for a pound
tondal := ton ft / s^2 // and for a ton
pdl := poundal
psi := pound force / inch^2
psia := psi // absolute pressure
tsi := ton force / inch^2
reyn := psi sec
lbf := lb force
slug := lbf s^2 / ft
slugf := slug force
slinch := lbf s^2 / inch // Mass unit derived from inch second
slinchf := slinch force // pound-force system. Used in space
// applications where in/sec^2 was a
// natural acceleration measure.
geepound := slug
tonf := ton force
lbm := lb
kip := 1000 lbf // from kilopound
mil := 1/1000 inch
thou := 1/1000inch
circularinch := 1/4 pi in^2 // area of a one-inch diameter circle
circularmil := 1/4 pi mil^2// area of one-mil diameter circle
cmil := circularmil
cental := 100 pound
centner := cental
caliber := 1/100 inch // for measuring bullets
duty := ft lbf
celo := ft / s^2
jerk := ft / s^3
australiapoint := 1/100 inch // The "point" is used to measure rainfall
// in Australia
sabin := ft^2 // Measure of sound absorption equal to the
// absorbing power of one square foot of
// a perfectly absorbing material. The
// sound absorptivity of an object is the
// area times a dimensionless
// absorptivity coefficient.
standardgauge := 4 ft + 8.5 in // Standard width between railroad track
flag := 5 ft^2 // Construction term referring to sidewalk.
rollwallpaper := 30 ft^2 // Area of roll of wall paper
fillpower := in^3 / ounce // Density of down at standard pressure.
// The best down has 750-800 fillpower.
pinlength := 1/16 inch // A//17 pin is 17/16 in long in the USA.
buttonline := 1/40 inch // The line was used in 19th century USA
// to measure width of buttons.
scoopnumber := quart^-1 // Ice cream scoops are labeled with a
// number specifying how many scoops
// fill a quart.
//
// Other units of work, energy, power, etc
//
// Btu definitions: energy to raise a pound of water 1 degF
// "Btu" is the correct capitalization.
Btu := cal lb degrankine / (gram K)// international table BTU
btu := Btu
BTU := btu
britishthermalunit := Btu
Btu_IT := Btu
btu_IT := Btu_IT
Btu_th := cal_th lb degrankine / (gram K)
btu_th := Btu_th
Btu_mean := cal_mean lb degrankine / (gram K)
btu_mean := Btu_mean
quad := quadrillion Btu
ECtherm := 105506000 J // Exact definition, close to 1e5 Btu
UStherm := 105480400 J // Exact definition
therm := UStherm
// The horsepower is supposedly the power of one horse pulling. Obviously
// different people had different horses.
horsepower := 550 foot pound force / sec // Invented by James Watt
hp := horsepower
metrichorsepower := 75 kilogram force meter / sec
electrichorsepower := 746 W
boilerhorsepower := 9809.50 W
waterhorsepower := 746.043 W
brhorsepower := 745.70 W
donkeypower := 250 W
Wh := watt hour
// Thermal insulance and conductivity.
Rvalue := degrankine ft^2 hr / Btu // r-value, U.S. insulation figure
Cvalue := 1/Rvalue // C-value U.S. insulation conductance rating
kvalue := Btu in / (ft^2 hr degF) // k-value, insulation conductance/in thick
Uvalue := 1/Rvalue
europeanUvalue := watt / (m^2 K)
RSI := K m^2 / W // SI insulation figure
// The following definitions are per NIST Special Publication 811:
// http://physics.nist.gov/Pubs/SP811/appenB9.html
W / (m K) ||| thermal_conductivity
m^2 K / W ||| thermal_insulance
K / W ||| thermal_resistance
m K / W ||| thermal_resistivity
// Term not defined by SI, somewhat questionable. Used in building trade.
W / (m^2 K) ||| thermal_conductance
// Defined by the BIPM,
// http://www.bipm.org/pdf/si-brochure.pdf
J/kg ||| specific_energy
W/m^2 ||| heat_flux_density
J/mol ||| molar_energy
J/(mol K) ||| molar_heat_capacity
// kvalue is defined as the amount of
// heat that will be transmitted through a one inch thick piece of
// homogenous material, one square foot in size, in one hour, when
// there is a one degree Fahrenheit temperature difference.
//
// Cvalue is the kvalue multiplied by the thickness in inches and thus
// gives the thermal conductance of a real piece of material with a given
// thickness.
// Rvalue is the reciprocal of this, and refers to the thermal insulance of a
// real piece of material of a given, concrete thickness.
clo := 0.155 K m^2 / W// Supposed to be the insulance
// required to keep a resting person
// comfortable indoors. The value
// given is from NIST and the CRC,
// but [5] gives a slightly different
// value of 0.875 ft^2 degF hr / Btu.
// Misc other measures
clausius := 1ee3 cal/K // A unit of physical entropy
langley := thermcalorie/cm^2
poncelet := 100 kg force m / s
tonrefrigeration := ton 144 Btu / (lb day)// One ton refrigeration is
// the rate of heat extraction required
// turn one ton of water to ice in
// a day. Ice is defined to have a
// latent heat of 144 Btu/lb.
tonref := tonrefrigeration
refrigeration := tonref / ton
frigorie := 1000 cal_fifteen// Used in refrigeration engineering.
// Energy in combustible fuels
TNT := 4_184_000_000 J/ton // So you can write tons TNT, this
// is a defined, not measured, value
PETN := 6.01e6 J/kg // An explosive compound,
// Pentaerythrite tetranitrate
// used in plastic explosive like Semtex
gasoline := 1.4e8 J/gallon // So you can convert energy
// to gallons gasoline
natural_gas := 1.09e6 J/foot^3 // Energy in natural gas
naturalgas := natural_gas
propane := 9.63e7 J/gallon // Energy in liquid propane
kerosene := 1.42e8 J/gallon // Energy in liquid kerosene
oil := 41.868 GJ/metricton
coal := 18.20 GJ/metricton
//
// Permeability: The permeability or permeance, n, of a substance determines
// how fast vapor flows through the substance. The formula W = n A dP
// holds where W is the rate of flow (in mass/time), n is the permeability,
// A is the area of the flow path, and dP is the vapor pressure difference.
//
// Alan's Veto: These are damned, damned sketchy, and are going to go.
// perm_0C := grain / (hr ft^2 inHg)
// perm_zero := perm_0C
// perm_0 := perm_0C
// perm := perm_0C
//perm_23C := grain / (hr ft^2 in-Hg23C)
//perm_twentythree := perm_23C
//
// Counting measures
//
unity := 1
pair := 2
couple := 2
brace := 2
nest := 3
dickers := 10
dozen := 12
bakersdozen := 13
score := 20
flock := 40
timer := 40
shock := 60
gross := 144
greatgross := 12 gross
// Paper counting measure
shortquire := 24
quire := 25
shortream := 480
ream := 500
perfectream := 516
bundle := 2 reams
bale := 5 bundles
//
// Paper measures
//
// USA paper sizes
lettersize := 8.5 inch 11 inch
legalsize := 8.5 inch 14 inch
ledgersize := 11 inch 17 inch
executivesize := 7.25 inch 10.5 inch
Apaper := 8.5 inch 11 inch
Bpaper := 11 inch 17 inch
Cpaper := 17 inch 22 inch
Dpaper := 22 inch 34 inch
Epaper := 34 inch 44 inch
// The metric paper sizes are defined so that if a sheet is cut in half
// along the short direction, the result is two sheets which are
// similar to the original sheet. This means that for any metric size,
// the long side is close to sqrt(2) times the length of the short
// side. Each series of sizes is generated by repeated cuts in half,
// with the values rounded down to the nearest millimeter.
A0paper := 841 mm 1189 mm // The basic size in the A series
A1paper := 594 mm 841 mm // is defined to have an area of
A2paper := 420 mm 594 mm // one square meter.
A3paper := 297 mm 420 mm
A4paper := 210 mm 297 mm
A5paper := 148 mm 210 mm
A6paper := 105 mm 148 mm
A7paper := 74 mm 105 mm
A8paper := 52 mm 74 mm
A9paper := 37 mm 52 mm
A10paper := 26 mm 37 mm
B0paper := 1000 mm 1414 mm // The basic B size has an area
B1paper := 707 mm 1000 mm // of sqrt(2) square meters.
B2paper := 500 mm 707 mm
B3paper := 353 mm 500 mm
B4paper := 250 mm 353 mm
B5paper := 176 mm 250 mm
B6paper := 125 mm 176 mm
B7paper := 88 mm 125 mm
B8paper := 62 mm 88 mm
B9paper := 44 mm 62 mm
B10paper := 31 mm 44 mm
C0paper := 917 mm 1297 mm // The basic C size has an area
C1paper := 648 mm 917 mm // of sqrt(sqrt(2)) square meters.
C2paper := 458 mm 648 mm
C3paper := 324 mm 458 mm // Intended for envelope sizes
C4paper := 229 mm 324 mm
C5paper := 162 mm 229 mm
C6paper := 114 mm 162 mm
C7paper := 81 mm 114 mm
C8paper := 57 mm 81 mm
C9paper := 40 mm 57 mm
C10paper := 28 mm 40 mm
// gsm (Grams per Square Meter), a sane, metric paper weight measure
gsm := grams / meter^2
// In the USA, a collection of crazy historical paper measures are used. Paper
// is measured as a weight of a ream of that particular type of paper. This is
// sometimes called the "substance" or "basis" (as in "substance 20" paper).
// The standard sheet size or "basis size" varies depending on the type of
// paper. As a result, 20 pound bond paper and 50 pound text paper are actually
// about the same weight. The different sheet sizes were historically the most
// convenient for printing or folding in the different applications. These
// different basis weights are standards maintained by American Society for
// Testing Materials (ASTM) and the American Forest and Paper Association
// (AF&PA).
poundbookpaper := lb / 25 inch 38 inch ream
lbbook := poundbookpaper
poundtextpaper := poundbookpaper
lbtext := poundtextpaper
poundoffsetpaper := poundbookpaper // For offset printing
lboffset := poundoffsetpaper
poundbiblepaper := poundbookpaper // Designed to be lightweight, thin,
lbbible := poundbiblepaper // strong and opaque.
poundtagpaper := lb / 24 inch 36 inch ream
lbtag := poundtagpaper
poundbagpaper := poundtagpaper
lbbag := poundbagpaper
poundnewsprintpaper := poundtagpaper
lbnewsprint := poundnewsprintpaper
poundposterpaper := poundtagpaper
lbposter := poundposterpaper
poundtissuepaper := poundtagpaper
lbtissue := poundtissuepaper
poundwrappingpaper := poundtagpaper
lbwrapping := poundwrappingpaper
poundwaxingpaper := poundtagpaper
lbwaxing := poundwaxingpaper
poundglassinepaper := poundtagpaper
lbglassine := poundglassinepaper
poundcoverpaper := lb / 20 inch 26 inch ream
lbcover := poundcoverpaper
poundindexpaper := lb / 25.5 inch 30.5 inch ream
lbindex := poundindexpaper
poundindexbristolpaper := poundindexpaper
lbindexbristol := poundindexpaper
poundbondpaper := lb / 17 inch 22 inch ream // Bond paper is stiff and
lbbond := poundbondpaper // durable for repeated
poundwritingpaper := poundbondpaper // filing, and it resists
lbwriting := poundwritingpaper // ink penetration.
poundledgerpaper := poundbondpaper
lbledger := poundledgerpaper
poundcopypaper := poundbondpaper
lbcopy := poundcopypaper
poundblottingpaper := lb / 19 inch 24 inch ream
lbblotting := poundblottingpaper
poundblankspaper := lb / 22 inch 28 inch ream
lbblanks := poundblankspaper
poundpostcardpaper := lb / 22.5 inch 28.5 inch ream
lbpostcard := poundpostcardpaper
poundweddingbristol := poundpostcardpaper
lbweddingbristol := poundweddingbristol
poundbristolpaper := poundweddingbristol
lbbristol := poundbristolpaper
poundboxboard := lb / (1000 ft^2)
lbboxboard := poundboxboard
poundpaperboard := poundboxboard
lbpaperboard := poundpaperboard
// When paper is marked in units of M, it means the weight of 1000 sheets of the
// given size of paper. To convert this to paper weight, divide by the size of
// the paper in question.
paperM := lb / 1000
//
// Old French distance measures, from French Weights and Measures
// Before the Revolution by Zupko
//
frenchfoot := 4500/13853 m // pied de roi, the standard of Paris.
pied := frenchfoot // Half of the hashimicubit,
frenchfeet := frenchfoot // instituted by Charlemagne.
frenchinch := 1/12 frenchfoot // This exact definition comes from
frenchthumb := frenchinch // a law passed on 10 Dec 1799 which
pouce := frenchthumb // fixed the meter at
// 3 frenchfeet + 11.296 lignes.
frenchline := 1/12 frenchinch // This is supposed to be the size
ligne := frenchline // of the average barleycorn
frenchpoint := 1/12 frenchline
toise := 6 frenchfeet
arpent := 180^2 pied^2 // The arpent is 100 square perches,
// but the perche seems to vary a lot
// and can be 18 feet, 20 feet, or 22
// feet. This measure was described
// as being in common use in Canada in
// 1934 (Websters 2nd). The value
// given here is the Paris standard
// arpent.
//
// Printing
//
fournierpoint := 0.1648 inch / 12 // First definition of the printers
// point made by Pierre Fournier who
// defined it in 1737 as 1/12 of a
// cicero which was 0.1648 inches.
olddidotpoint := 1/72 frenchinch // François Ambroise Didot, one of
// a family of printers, changed
// Fournier's definition around 1770
// to fit to the French units then in
// use.
bertholdpoint := 1/2660 m // H. Berthold tried to create a
// metric version of the didot point
// in 1878.
INpoint := 0.4 mm // This point was created by a
// group directed by Fermin Didot in
// 1881 and is associated with the
// imprimerie nationale. It doesn't
// seem to have been used much.
germandidotpoint := 0.376065 mm // Exact definition appears in DIN
// 16507, a German standards document
// of 1954. Adopted more broadly in
// 1966 by ???
metricpoint := 3/8 mm // Proposed in 1977 by Eurograf
point := 13837/1000000 inch // exact, NIST Handbook 44, Appendix 3
printerspoint := point
texscaledpoint := 1/65536 point // The TeX typesetting system uses
texsp := texscaledpoint // this for all computations.
computerpoint := 1/72 inch // The American point was rounded
computerpica := 12 computerpoint // to an even 1/72 inch by computer
postscriptpoint := computerpoint // people at some point.
pspoint := postscriptpoint
Q := 1/4 mm // Used in Japanese phototypesetting
// Q is for quarter
frenchprinterspoint := olddidotpoint
didotpoint := germandidotpoint // This seems to be the dominant value
europeanpoint := didotpoint // for the point used in Europe
cicero := 12 didotpoint
stick := 2 inches
// Type sizes
excelsior := 3 point
brilliant := 3.5 point
diamond := 4 point
pearl := 5 point
agate := 5.5 point
ruby := agate // British
nonpareil := 6 point
mignonette := 6.5 point
emerald := mignonette// British
minion := 7 point
brevier := 8 point
bourgeois := 9 point
longprimer := 10 point
smallpica := 11 point
pica := 12 point
english := 14 point
columbian := 16 point
greatprimer := 18 point
paragon := 20 point
meridian := 44 point
canon := 48 point
// German type sizes
nonplusultra := 2 didotpoint
brillant := 3 didotpoint
diamant := 4 didotpoint
perl := 5 didotpoint
nonpareille := 6 didotpoint
kolonel := 7 didotpoint
petit := 8 didotpoint
borgis := 9 didotpoint
korpus := 10 didotpoint
corpus := korpus
garamond := korpus
mittel := 14 didotpoint
tertia := 16 didotpoint
text := 18 didotpoint
kleine_kanon := 32 didotpoint
kanon := 36 didotpoint
grosse_kanon := 42 didotpoint
missal := 48 didotpoint
kleine_sabon := 72 didotpoint
grosse_sabon := 84 didotpoint
//
// Information theory units
//
nat := 0.69314718056 bits // Entropy measured base e
hartley := 3.32192809488 bits // log2(10) bits, or the entropy
// of a uniformly distributed
// random variable over 10
// symbols.
//
// Computer
//
bps := bit/sec // Sometimes the term "baud" is
// incorrectly used to refer to
// bits per second. Baud refers
// to symbols per second. Modern
// modems transmit several bits
// per symbol.
byte := 8 bit // Not all machines had 8 bit
// bytes, but these days most of
// them do. But beware: for
// transmission over modems, a
// few extra bits are used so
// there are actually 10 bits per
// byte.
nybble := 4 bits // Half of a byte. Sometimes
// equal to different lengths
// such as 3 bits.
nibble := nybble
// In computers, "kilo" tends to mean a multiple of 1024 or 2^10.
// This obviously interferes with the standard meanings.
//
// In December 1998 the International Electrotechnical Commission (IEC), the
// leading international organization for worldwide standardization in
// electrotechnology, approved as an IEC International Standard names and
// symbols for prefixes for binary multiples for use in the fields of data
// processing and data transmission. One would say "kibibit" to mean 1024 bits
//
// http://physics.nist.gov/cuu/Units/binary.html
// Prefixes
kibi ::- 2^10 // kilobinary
mebi ::- 2^20 // megabinary
gibi ::- 2^30 // gigabinary
tebi ::- 2^40 // terabinary
pebi ::- 2^50 // petabinary
exbi ::- 2^60 // exabinary
// Official symbols
Ki :- kibi
Mi :- mebi
Gi :- gibi
Ti :- tebi
Pi :- pebi
Ei :- exbi
jiffy := 1/100 sec // This is defined in the Jargon File
jiffies := jiffy // (http://www.jargon.org) as being the
// duration of a clock tick for measuring
// wall-clock time. Supposedly the value
// used to be 1/60 sec or 1/50 sec
// depending on the frequency of AC power,
// but then 1/100 sec became more common.
// On linux systems, this term is used and
// for the Intel based chips, it does have
// the value of .01 sec. The Jargon File
// also lists two other definitions:
// millisecond, and the time taken for
// light to travel one foot.
//
// yarn and cloth measures
//
// yarn linear density
m kg^-1 ||| reciprocal_linear_mass_density
woolyarnrun := 1600 yard/pound// 1600 yds of "number 1 yarn" weighs
// a pound.
yarncut := 300 yard/pound // Less common system used in
// Pennsylvania for wool yarn
cottonyarncount := 840 yard/pound
linenyarncount := 300 yard/pound // Also used for hemp and ramie
worstedyarncount := 1680 ft/pound
metricyarncount := meter/gram
kg/m ||| linear_mass_density
tex := gram / km // rational metric yarn measure, meant
denier := 1/9 tex // used for silk and rayon
manchesteryarnnumber := drams/(1000 yards)// old system used for silk
pli := lb/in
typp := 1000 yd/lb
asbestoscut := 100 yd/lb // used for glass and asbestos yarn
drex := 0.1 tex // to be used for any kind of yarn
// yarn and cloth length
skeincotton := 80*54 inch // 80 turns of thread on a reel with a
// 54 in circumference (varies for other
// kinds of thread)
cottonbolt := 120 ft // cloth measurement
woolbolt := 210 ft
bolt := cottonbolt
heer := 600 yards
cut := 300 yards // used for wet-spun linen yarn
lea := 300 yards
//
// drug dosage
//
mcg := microgram // Frequently used for vitamins
iudiptheria := 62.8 microgram // IU is for international unit
iupenicillin := 0.6 microgram
iuinsulin := 41.67 microgram
drop := 1/20 ml // The drop was an old "unit" that was
// replaced by the minim. But I was
// told by a pharmacist that in his
// profession, the conversion of 20
// drops per ml is actually used.
bloodunit := 450 ml // For whole blood. For blood
// components, a blood unit is the
// quanity of the component found in a
// blood unit of whole blood. The
// human body contains about 12 blood
// units of whole blood.
//
// fixup units for times when prefix handling doesn't do the job
//
hectare := hectoare
ha := hectare
megohm := megaohm
kilohm := kiloohm
microhm := microohm
cent := 1/100 dollar
// British currency
//
// These have been supplanted by the PoundSource definitions which include
// historical exchange rates for years back to 1600.
//
//shilling := 1/20 britainpound // Before decimalisation, there
//oldpence := 1/12 shilling // were 20 shillings to a pound,
// each of twelve old pence
//quid := britainpound // Slang names
//fiver := 5 quid
//tenner := 10 quid
//
// Units used for measuring volume of wood
//
cord := 4 ft * 4 ft * 8 ft// 4 ft by 4 ft by 8 ft bundle of wood
facecord := 1/2 cord
cordfoot := 1/8 cord // One foot long section of a cord
cordfeet := cordfoot
rick := 4 ft 8 ft 16 inches // Stack of firewood
housecord := 1/3 cord // Used to sell firewood for residences,
// often confusingly called a "cord"
boardfoot := ft^2 inch // Usually 1 inch thick wood
boardfeet := boardfoot
fbm := boardfoot // feet board measure
stere := m^3
st := stere
timberfoot := ft^3 // Used for measuring solid blocks of wood
standard := 120 12 ft 11 in 1.5 in // This is the St Petersburg or
// Pittsburg standard. Apparently the
// term is short for "standard hundred"
// which was meant to refer to 100 pieces
// of wood (deals). However, this
// particular standard is equal to 120
// deals which are 12 ft by 11 in by 1.5
// inches (not the standard deal).
// In Britain, the deal is apparently any piece of wood over 6 feet long, over
// 7 wide and 2.5 inches thick. The OED doesn't give a standard size. A piece
// of wood less than 7 inches wide is called a "batten". This unit is now used
// exclusively for fir and pine.
deal := 12 ft 11 in 2.5 in // The standard North American deal [OED]
wholedeal := 1/2 deal // If it's half as thick as the standard
// deal it's called a "whole deal"!
splitdeal := 1/2 wholedeal // And half again as thick is a split deal.
//
// Gas and Liquid flow units
//
// Some horribly-named flow units that I've never seen used other than once
// (unexplained) in the Guinness Book of World Records which has degraded into
// tabloid trash.
cumec := m^3/s
cusec := ft^3/s
// Conventional abbreviations for fluid flow units
gph := gal/hr
gpm := gal/min
mgd := megagal/day
cfs := ft^3/s
cfh := ft^3/hour
cfm := ft^3/min
lpm := liter/min
// Miner's inch: This is an old historic unit used in the Western United
// States. It is generally defined as the rate of flow through a one square
// inch hole at a specified depth such as 4 inches. In the late 19th century,
// volume of water was sometimes measured in the "24 hour inch". Values for the
// miner's inch were fixed by state statues. (This information is from a web
// site operated by the Nevada Division of Water Planning: The Water Words
// Dictionary at http://www.state.nv.us/cnr/ndwp/dict-1/waterwds.htm.)
minersinchAZ := 1.5 ft^3/min
minersinchCA := 1.5 ft^3/min
minersinchMT := 1.5 ft^3/min
minersinchNV := 1.5 ft^3/min
minersinchOR := 1.5 ft^3/min
minersinchID := 1.2 ft^3/min
minersinchKS := 1.2 ft^3/min
minersinchNE := 1.2 ft^3/min
minersinchNM := 1.2 ft^3/min
minersinchND := 1.2 ft^3/min
minersinchSD := 1.2 ft^3/min
minersinchUT := 1.2 ft^3/min
minersinchCO := 1.56 ft^3/min
minersinchBC := 1.68 ft^3/min // British Columbia
// In vacuum science and some other applications, gas flow is measured
// as the product of volumetric flow and pressure. This is useful
// because it makes it easy to compare with the flow at standard
// pressure (one atmosphere). It also directly relates to the number
// of gas molecules per unit time, and hence to the mass flow if the
// molecular mass is known.
sccm := atm cc/min // 's' is for "standard" to indicate
sccs := atm cc/sec // flow at standard pressure
scfh := atm ft^3/hour //
scfm := atm ft^3/min
slpm := atm liter/min
slph := atm liter/hour
lusec := liter micron Hg force / s // Used in vacuum science
// Wire gauge: this area is a nightmare with huge charts of wire gauge
// diameters that usually have no clear origin. There are at least 5 competing
// wire gauge systems to add to the confusion.
// The use of wire gauge is related to the manufacturing method: a metal rod is
// heated and drawn through a hole. The size change can't be too big. To get
// smaller wires, the process is repeated with a series of smaller holes.
// American Wire Gauge (AWG) or Brown & Sharpe Gauge appears to be the most
// important gauge. ASTM B-258 specifies that this gauge is based on geometric
// interpolation between gauge 0000, which is 0.46 inches exactly, and gauge 36
// which is 0.005 inches exactly. Therefore, the diameter in inches of a wire
// is given by the formula 1/200 92^((36-g)/39). Note that 92^(1/39) is close
// to 2^(1/6), so diameter is approximately halved for every 6 gauges. For the
// repeated zero values, use negative numbers in the formula. The same document
// also specifies rounding rules which seem to be ignored by makers of tables.
// Gauges up to 44 are to be specified with up to 4 significant figures, but no
// closer than 0.0001 inch. Gauges from 44 to 56 are to be rounded to the
// nearest 0.00001 inch. The table below gives 4 significant figures for all
// gauges.
//
// In addition to being used to measure wire thickness, this gauge is used to
// measure the thickness of sheets of aluminum, copper, and most metals other
// than steel, iron and zinc.
// The numbers below are DIAMETERS.
wire0000gauge := 0.4600 in
wire000gauge := 0.4096 in
wire00gauge := 0.3648 in
wire0gauge := 0.3249 in
wire1gauge := 0.2893 in
wire2gauge := 0.2576 in
wire3gauge := 0.2294 in
wire4gauge := 0.2043 in
wire5gauge := 0.1819 in
wire6gauge := 0.1620 in
wire7gauge := 0.1443 in
wire8gauge := 0.1285 in
wire9gauge := 0.1144 in
wire10gauge := 0.1019 in
wire11gauge := 0.09074 in
wire12gauge := 0.08081 in
wire13gauge := 0.07196 in
wire14gauge := 0.06408 in
wire15gauge := 0.05707 in
wire16gauge := 0.05082 in
wire17gauge := 0.04526 in
wire18gauge := 0.04030 in
wire19gauge := 0.03589 in
wire20gauge := 0.03196 in
wire21gauge := 0.02846 in
wire22gauge := 0.02535 in
wire23gauge := 0.02257 in
wire24gauge := 0.02010 in
wire25gauge := 0.01790 in
wire26gauge := 0.01594 in
wire27gauge := 0.01420 in
wire28gauge := 0.01264 in
wire29gauge := 0.01126 in
wire30gauge := 0.01003 in
wire31gauge := 0.008928 in
wire32gauge := 0.007950 in
wire33gauge := 0.007080 in
wire34gauge := 0.006305 in
wire35gauge := 0.005615 in
wire36gauge := 0.005000 in
wire37gauge := 0.004453 in
wire38gauge := 0.003965 in
wire39gauge := 0.003531 in
wire40gauge := 0.003145 in
wire41gauge := 0.002800 in
wire42gauge := 0.002494 in
wire43gauge := 0.002221 in
wire44gauge := 0.001978 in
wire45gauge := 0.001761 in
wire46gauge := 0.001568 in
wire47gauge := 0.001397 in
wire48gauge := 0.001244 in
wire49gauge := 0.001108 in
wire50gauge := 0.0009863 in
wire51gauge := 0.0008783 in
wire52gauge := 0.0007822 in
wire53gauge := 0.0006966 in
wire54gauge := 0.0006203 in
wire55gauge := 0.0005524 in
wire56gauge := 0.0004919 in
// Next we have the SWG, the Imperial or British Standard Wire Gauge. This one
// is piecewise linear, so it is not generated by a simple formula. It was used
// for aluminum sheets.
brwire0000000gauge := 0.500 in
brwire000000gauge := 0.464 in
brwire00000gauge := 0.432 in
brwire0000gauge := 0.400 in
brwire000gauge := 0.372 in
brwire00gauge := 0.348 in
brwire0gauge := 0.324 in
brwire1gauge := 0.300 in
brwire2gauge := 0.276 in
brwire3gauge := 0.252 in
brwire4gauge := 0.232 in
brwire5gauge := 0.212 in
brwire6gauge := 0.192 in
brwire7gauge := 0.176 in
brwire8gauge := 0.160 in
brwire9gauge := 0.144 in
brwire10gauge := 0.128 in
brwire11gauge := 0.116 in
brwire12gauge := 0.104 in
brwire13gauge := 0.092 in
brwire14gauge := 0.080 in
brwire15gauge := 0.072 in
brwire16gauge := 0.064 in
brwire17gauge := 0.056 in
brwire18gauge := 0.048 in
brwire19gauge := 0.040 in
brwire20gauge := 0.036 in
brwire21gauge := 0.032 in
brwire22gauge := 0.028 in
brwire23gauge := 0.024 in
brwire24gauge := 0.022 in
brwire25gauge := 0.0200 in
brwire26gauge := 0.0180 in
brwire27gauge := 0.0164 in
brwire28gauge := 0.0149 in
brwire29gauge := 0.0136 in
brwire30gauge := 0.0124 in
brwire31gauge := 0.0116 in
brwire32gauge := 0.0108 in
brwire33gauge := 0.0100 in
brwire34gauge := 0.0092 in
brwire35gauge := 0.0084 in
brwire36gauge := 0.0076 in
brwire37gauge := 0.0068 in
brwire38gauge := 0.0060 in
brwire39gauge := 0.0052 in
brwire40gauge := 0.0048 in
brwire41gauge := 0.0044 in
brwire42gauge := 0.0040 in
brwire43gauge := 0.0036 in
brwire44gauge := 0.0032 in
brwire45gauge := 0.0028 in
brwire46gauge := 0.0024 in
brwire47gauge := 0.0020 in
brwire48gauge := 0.0016 in
brwire49gauge := 0.0012 in
brwire50gauge := 0.0010 in
// The following is from the Appendix to ASTM B 258
//
// For example, in U.S. gage, the standard for sheet metal is based on the
// weight of the metal, not on the thickness. 16-gage is listed as approximately
// .0625 inch thick and 40 ounces per square foot (the original standard was
// based on wrought iron at .2778 pounds per cubic inch; steel has almost
// entirely superseded wrought iron for sheet use, at .2833 pounds per cubic
// inch). Smaller numbers refer to greater thickness. There is no formula for
// converting gage to thickness or weight.
//
// It's rather unclear from the passage above whether the plate gauge values are
// therefore wrong if steel is being used. Reference [15] states that steel is
// in fact measured using this gauge (under the name Manufacturers' Standard
// Gauge) with a density of 501.84 lb/ft3 = 0.2904 lb/in3 used for steel.
// But this doesn't seem to be the correct density of steel (.2833 lb/in3 is
// closer), and nobody else lists these values.
//
// This gauge was established in 1893 for purposes of taxation.
plate000000gauge := 15/32 in // 300 oz / ft^2
plate00000gauge := 14/32 in // 280 oz / ft^2
plate0000gauge := 13/32 in // 260 oz / ft^2
plate000gauge := 12/32 in // 240 oz / ft^2
plate00gauge := 11/32 in // 220 oz / ft^2
plate0gauge := 10/32 in // 200 oz / ft^2
plate1gauge := 9/32 in // 180 oz / ft^2
plate2gauge := 17/64 in // 170 oz / ft^2
plate3gauge := 16/64 in // 160 oz / ft^2
plate4gauge := 15/64 in // 150 oz / ft^2
plate5gauge := 14/64 in // 140 oz / ft^2
plate6gauge := 13/64 in // 130 oz / ft^2
plate7gauge := 12/64 in // 120 oz / ft^2
plate8gauge := 11/64 in // 110 oz / ft^2
plate9gauge := 10/64 in // 100 oz / ft^2
plate10gauge := 9/64 in // 90 oz / ft^2
plate11gauge := 8/64 in // 80 oz / ft^2
plate12gauge := 7/64 in // 70 oz / ft^2
plate13gauge := 6/64 in // 60 oz / ft^2
plate14gauge := 5/64 in // 50 oz / ft^2
plate15gauge := 9/128 in // 45 oz / ft^2
plate16gauge := 8/128 in // 40 oz / ft^2
plate17gauge := 9/160 in // 36 oz / ft^2
plate18gauge := 8/160 in // 32 oz / ft^2
plate19gauge := 7/160 in // 28 oz / ft^2
plate20gauge := 6/160 in // 24 oz / ft^2
plate21gauge := 11/320 in // 22 oz / ft^2
plate22gauge := 10/320 in // 20 oz / ft^2
plate23gauge := 9/320 in // 18 oz / ft^2
plate24gauge := 8/320 in // 16 oz / ft^2
plate25gauge := 7/320 in // 14 oz / ft^2
plate26gauge := 6/320 in // 12 oz / ft^2
plate27gauge := 11/640 in // 11 oz / ft^2
plate28gauge := 10/640 in // 10 oz / ft^2
plate29gauge := 9/640 in // 9 oz / ft^2
plate30gauge := 8/640 in // 8 oz / ft^2
plate31gauge := 7/640 in // 7 oz / ft^2
plate32gauge := 13/1280 in // 6.5 oz / ft^2
plate33gauge := 12/1280 in // 6 oz / ft^2
plate34gauge := 11/1280 in // 5.5 oz / ft^2
plate35gauge := 10/1280 in // 5 oz / ft^2
plate36gauge := 9/1280 in // 4.5 oz / ft^2
plate37gauge := 17/2560 in // 4.25 oz / ft^2
plate38gauge := 16/2560 in // 4 oz / ft^2
// Zinc sheet metal gauge
zinc1gauge := 0.002 in
zinc2gauge := 0.004 in
zinc3gauge := 0.006 in
zinc4gauge := 0.008 in
zinc5gauge := 0.010 in
zinc6gauge := 0.012 in
zinc7gauge := 0.014 in
zinc8gauge := 0.016 in
zinc9gauge := 0.018 in
zinc10gauge := 0.020 in
zinc11gauge := 0.024 in
zinc12gauge := 0.028 in
zinc13gauge := 0.032 in
zinc14gauge := 0.036 in
zinc15gauge := 0.040 in
zinc16gauge := 0.045 in
zinc17gauge := 0.050 in
zinc18gauge := 0.055 in
zinc19gauge := 0.060 in
zinc20gauge := 0.070 in
zinc21gauge := 0.080 in
zinc22gauge := 0.090 in
zinc23gauge := 0.100 in
zinc24gauge := 0.125 in
zinc25gauge := 0.250 in
zinc26gauge := 0.375 in
zinc27gauge := 0.500 in
zinc28gauge := 1.000 in
// USA ring sizes. Several slightly different definitions seem to be in
// circulation. According to [15], the interior diameter of size n ring in
// inches is 0.32 n + 0.458 for n ranging from 3 to 13.5 by steps of 0.5. The
// size 2 ring is inconsistently 0.538in and no 2.5 size is listed.
//
// However, other sources list 0.455 + 0.0326 n and 0.4525 + 0.0324 n as the
// diameter and list no special case for size 2. (Or alternatively they are
// 1.43 + .102 n and 1.4216+.1018 n for measuring circumference in inches.) One
// reference claimed that the original system was that each size was 1/10 inch
// circumference, but that source doesn't have an explanation for the modern
// system which is somewhat different.
//
// This table gives circumferences as listed in [15].
size2ring := 0.538 in pi
size3ring := 0.554 in pi
size3_5ring := 0.570 in pi
size4ring := 0.586 in pi
size4_5ring := 0.602 in pi
size5ring := 0.618 in pi
size5_5ring := 0.634 in pi
size6ring := 0.650 in pi
size6_5ring := 0.666 in pi
size7ring := 0.682 in pi
size7_5ring := 0.698 in pi
size8ring := 0.714 in pi
size8_5ring := 0.730 in pi
size9ring := 0.746 in pi
size9_5ring := 0.762 in pi
size10ring := 0.778 in pi
size10_5ring := 0.794 in pi
size11ring := 0.810 in pi
size11_5ring := 0.826 in pi
size12ring := 0.842 in pi
size12_5ring := 0.858 in pi
size13ring := 0.874 in pi
size13_5ring := 0.890 in pi
// Old practice in the UK measured rings using the "Wheatsheaf gauge" with sizes
// specified alphabetically and based on the ring inside diameter in steps of
// 1/64 inch. This system was replaced in 1987 by British Standard 6820 which
// specifies sizes based on circumference. Each size is 1.25 mm different from
// the preceding size. The baseline is size C which is 40 mm circumference.
// The new sizes are close to the old ones. Sometimes it's necessary to go
// beyond size Z to Z+1, Z+2, etc.
sizeAring := 37.50 mm
sizeBring := 38.75 mm
sizeCring := 40.00 mm
sizeDring := 41.25 mm
sizeEring := 42.50 mm
sizeFring := 43.75 mm
sizeGring := 45.00 mm
sizeHring := 46.25 mm
sizeIring := 47.50 mm
sizeJring := 48.75 mm
sizeKring := 50.00 mm
sizeLring := 51.25 mm
sizeMring := 52.50 mm
sizeNring := 53.75 mm
sizeOring := 55.00 mm
sizePring := 56.25 mm
sizeQring := 57.50 mm
sizeRring := 58.75 mm
sizeSring := 60.00 mm
sizeTring := 61.25 mm
sizeUring := 62.50 mm
sizeVring := 63.75 mm
sizeWring := 65.00 mm
sizeXring := 66.25 mm
sizeYring := 67.50 mm
sizeZring := 68.75 mm
// Japanese sizes start with size 1 at a 13mm inside diameter and each size is
// 1/3 mm larger in diameter than the previous one. They are multiplied by pi
// to give circumference.
jpsize1ring := 39/3 pi mm
jpsize2ring := 40/3 pi mm
jpsize3ring := 41/3 pi mm
jpsize4ring := 42/3 pi mm
jpsize5ring := 43/3 pi mm
jpsize6ring := 44/3 pi mm
jpsize7ring := 45/3 pi mm
jpsize8ring := 46/3 pi mm
jpsize9ring := 47/3 pi mm
jpsize10ring := 48/3 pi mm
jpsize11ring := 49/3 pi mm
jpsize12ring := 50/3 pi mm
jpsize13ring := 51/3 pi mm
jpsize14ring := 52/3 pi mm
jpsize15ring := 53/3 pi mm
jpsize16ring := 54/3 pi mm
jpsize17ring := 55/3 pi mm
jpsize18ring := 56/3 pi mm
jpsize19ring := 57/3 pi mm
jpsize20ring := 58/3 pi mm
jpsize21ring := 59/3 pi mm
jpsize22ring := 60/3 pi mm
jpsize23ring := 61/3 pi mm
jpsize24ring := 62/3 pi mm
jpsize25ring := 63/3 pi mm
jpsize26ring := 64/3 pi mm
jpsize27ring := 65/3 pi mm
jpsize28ring := 66/3 pi mm
jpsize29ring := 67/3 pi mm
jpsize30ring := 68/3 pi mm
// The European ring sizes are the length of the circumference in mm minus 40.
eusize1ring := 41 mm
eusize2ring := 42 mm
eusize3ring := 43 mm
eusize4ring := 44 mm
eusize5ring := 45 mm
eusize6ring := 46 mm
eusize7ring := 47 mm
eusize8ring := 48 mm
eusize9ring := 49 mm
eusize10ring := 50 mm
eusize11ring := 51 mm
eusize12ring := 52 mm
eusize13ring := 53 mm
eusize14ring := 54 mm
eusize15ring := 55 mm
eusize16ring := 56 mm
eusize17ring := 57 mm
eusize18ring := 58 mm
eusize19ring := 59 mm
eusize20ring := 60 mm
eusize21ring := 61 mm
eusize22ring := 62 mm
eusize23ring := 63 mm
eusize24ring := 64 mm
eusize25ring := 65 mm
eusize26ring := 66 mm
eusize27ring := 67 mm
eusize28ring := 68 mm
eusize29ring := 69 mm
eusize30ring := 70 mm
//
// Abbreviations
//
mph := mile/hr
mpg := mile/gal
kph := km/hr
fL := footlambert
fpm := ft/min
fps := ft/s
rpm := rev/min
rps := rev/sec
mi := mile
mbh := 1ee3 Btu/hour
mcm := 1ee3 circularmil
//
// Radioactivity units
//
becquerel := s^-1 // Activity of radioactive source
Bq := becquerel //
curie := 37ee9 Bq // Defined in 1910 as the radioactivity
Ci := curie // emitted by the amount of radon that is
// in equilibrium with 1 gram of radium.
rutherford := 1ee6 Bq //
gray := J/kg // Absorbed dose of radiation
Gy := gray //
rad := 1ee-2 Gy // From Radiation Absorbed Dose
rep := 8.38 mGy // Roentgen Equivalent Physical, the amount
// of radiation which , absorbed in the
// body, would liberate the same amount
// of energy as 1 roentgen of X rays
// would, or 97 ergs.
sievert := J/kg // Dose equivalent: dosage that has the
Sv := sievert // same effect on human tissues as 200
rem := 1ee-2 Sv // keV X-rays. Different types of
// radiation are weighted by the
// Relative Biological Effectiveness
// (RBE).
//
// Radiation type RBE
// X-ray, gamma ray 1
// beta rays, > 1 MeV 1
// beta rays, < 1 MeV 1.08
// neutrons, < 1 MeV 4-5
// neutrons, 1-10 MeV 10
// protons, 1 MeV 8.5
// protons, .1 MeV 10
// alpha, 5 MeV 15
// alpha, 1 MeV 20
//
// The energies are the kinetic energy
// of the particles. Slower particles
// interact more, so they are more
// effective ionizers, and hence have
// higher RBE values.
//
// rem stands for Roentgen Equivalent
// Mammal
roentgen := 258ee-6 C / kg // Ionizing radiation that produces
// 1 statcoulomb of charge in 1 cc of
// dry air at stp.
rontgen := roentgen // Sometimes it appears spelled this way
sievertunit := 8.38 rontgen // Unit of gamma ray dose delivered in one
// hour at a distance of 1 cm from a
// point source of 1 mg of radium
// enclosed in platinum .5 mm thick.
eman := 1ee-7 Ci/m^3 // radioactive concentration
mache := 3.7e-7 Ci/m^3
//
// Atomic weights. The atomic weight of an element is the ratio of the mass of
// a mole of the element to 1/12 of a mole of Carbon 12. The Standard Atomic
// Weights apply to the elements as they occur naturally on earth. Elements
// which do not occur naturally or which occur with wide isotopic variability do
// not have Standard Atomic Weights. For these elements, the atomic weight is
// based on the longest lived isotope, as marked in the comments. In some
// cases, the comment for these entries also gives a number which is an atomic
// weight for a different isotope that may be of more interest than the longest
// lived isotope.
//
g/mol ||| molar_mass
actinium := 227.0278 g/mol
aluminum := 26.981539 g/mol
aluminium := aluminum
americium := 243.0614 g/mol // Longest lived. 241.06
antimony := 121.760 g/mol
argon := 39.948 g/mol
arsenic := 74.92159 g/mol
astatine := 209.9871 g/mol // Longest lived
barium := 137.327 g/mol
berkelium := 247.0703 g/mol // Longest lived. 249.08
beryllium := 9.012182 g/mol
bismuth := 208.98037 g/mol
boron := 10.811 g/mol
bromine := 79.904 g/mol
cadmium := 112.411 g/mol
calcium := 40.078 g/mol
californium := 251.0796 g/mol // Longest lived. 252.08
carbon := 12.011 g/mol
cerium := 140.115 g/mol
cesium := 132.90543 g/mol
chlorine := 35.4527 g/mol
chromium := 51.9961 g/mol
cobalt := 58.93320 g/mol
copper := 63.546 g/mol
curium := 247.0703 g/mol
dysprosium := 162.50 g/mol
einsteinium := 252.083 g/mol // Longest lived
erbium := 167.26 g/mol
europium := 151.965 g/mol
fermium := 257.0951 g/mol // Longest lived
fluorine := 18.9984032 g/mol
francium := 223.0197 g/mol // Longest lived
gadolinium := 157.25 g/mol
gallium := 69.723 g/mol
germanium := 72.61 g/mol
gold := 196.96654 g/mol
hafnium := 178.49 g/mol
helium := 4.002602 g/mol
holmium := 164.93032 g/mol
hydrogen := 1.00794 g/mol
indium := 114.818 g/mol
iodine := 126.90447 g/mol
iridium := 192.217 g/mol
iron := 55.845 g/mol
krypton := 83.80 g/mol
lanthanum := 138.9055 g/mol
lawrencium := 262.11 g/mol // Longest lived
lead := 207.2 g/mol
lithium := 6.941 g/mol
lutetium := 174.967 g/mol
magnesium := 24.3050 g/mol
manganese := 54.93805 g/mol
mendelevium := 258.10 g/mol // Longest lived
mercury := 200.59 g/mol
molybdenum := 95.94 g/mol
neodymium := 144.24 g/mol
neon := 20.1797 g/mol
neptunium := 237.0482 g/mol
nickel := 58.6934 g/mol
niobium := 92.90638 g/mol
nitrogen := 14.00674 g/mol
nobelium := 259.1009 g/mol // Longest lived
osmium := 190.23 g/mol
oxygen := 15.9994 g/mol
palladium := 106.42 g/mol
phosphorus := 30.973762 g/mol
platinum := 195.08 g/mol
plutonium := 244.0642 g/mol // Longest lived. 239.05
polonium := 208.9824 g/mol // Longest lived. 209.98
potassium := 39.0983 g/mol
praseodymium := 140.90765 g/mol
promethium := 144.9127 g/mol // Longest lived. 146.92
protactinium := 231.03588 g/mol
radium := 226.0254 g/mol
radon := 222.0176 g/mol // Longest lived
rhenium := 186.207 g/mol
rhodium := 102.90550 g/mol
rubidium := 85.4678 g/mol
ruthenium := 101.07 g/mol
samarium := 150.36 g/mol
scandium := 44.955910 g/mol
selenium := 78.96 g/mol
silicon := 28.0855 g/mol
silver := 107.8682 g/mol
sodium := 22.989768 g/mol
strontium := 87.62 g/mol
sulfur := 32.066 g/mol
sulphur := sulfur
tantalum := 180.9479 g/mol
technetium := 97.9072 g/mol // Longest lived. 98.906
tellurium := 127.60 g/mol
terbium := 158.92534 g/mol
thallium := 204.3833 g/mol
thorium := 232.0381 g/mol
thullium := 168.93421 g/mol
tin := 118.710 g/mol
titanium := 47.867 g/mol
tungsten := 183.84 g/mol
uranium := 238.0289 g/mol
vanadium := 50.9415 g/mol
xenon := 131.29 g/mol
ytterbium := 173.04 g/mol
yttrium := 88.90585 g/mol
zinc := 65.39 g/mol
zirconium := 91.224 g/mol
//
// Before the Imperial Weights and Measures Act of 1824, various different
// weights and measures were in use in different places.
//
// Scots linear measure
scotsinch := 1.00540054 britishinch
scotsell := 37 scotsinch
scotsfall := 6 scotsell
scotschain := 4 scotsfall
scotslink := 1/100 scotschain
scotsfoot := 12 scotsinch
scotsfeet := scotsfoot
scotsfurlong := 10 scotschain
scotsmile := 8 scotsfurlong
// Scots area measure
scotsrood := 40 scotsfall^2
scotsacre := 4 scotsrood
// Irish linear measure
irishinch := britishinch
irishpalm := 3 irishinch
irishspan := 3 irishpalm
irishfoot := 12 irishinch
irishfeet := irishfoot
irishcubit := 18 irishinch
irishyard := 3 irishfeet
irishpace := 5 irishfeet
irishfathom := 6 irishfeet
irishpole := 7 irishyard // Only these values
irishperch := irishpole // are different from
irishchain := 4 irishperch // the British Imperial
irishlink := 1/100 irishchain// or English values for
irishfurlong :=10 irishchain // these lengths.
irishmile := 8 irishfurlong //
// Irish area measure
irishrood := 40 irishpole^2
irishacre := 4 irishrood
// Modern US Beer capacity
beerbarrel := 31 gallons // A full beer barrel
keg := 1/2 beerbarrel // The standard "keg" is a half barrel
beerkeg := keg
ponykeg := 1/2 keg
case := 24 12 floz // Why not?
beercase := case
// English wine capacity measures (Winchester measures)
winegallon := 231 britishinch^3 // Sometimes called the Winchester Wine Gallon,
// it was legalized in 1707 by Queen Anne, and
// given the definition of 231 cubic inches. It
// had been in use for a while as 8 pounds of wine
// using a merchant's pound of 7200 grains or
// 15 troy ounces. (The old mercantile pound had
// been 15 tower ounces.)
winequart := 1/4 winegallon
winepint := 1/2 winequart
winerundlet :=18 winegallon
winebarrel := 31.5 winegallon
winetierce := 42 winegallon
winehogshead := 2 winebarrel
winepuncheon := 2 winetierce
winebutt := 2 winehogshead
winepipe := winebutt
winetun := 2 winebutt
// English beer and ale measures used 1803-1824 and used for beer before 1688
englishbeergallon := 282 britishinch^3
englishbeerquart := 1/4 englishbeergallon
englishbeerpint := 1/2 englishbeerquart
englishbeerbarrel := 36 englishbeergallon
englishbeerhogshead := 1.5 englishbeerbarrel
// English ale measures used from 1688-1803 for both ale and beer
alegallon := englishbeergallon
alequart := 1/4 alegallon
alepint := 1/2 alequart
alebarrel := 34 alegallon
alehogshead :=1.5 alebarrel
// Scots capacity measure
scotsgallon :=827.232 britishinch^3
scotsquart := 1/4 scotsgallon
scotspint := 1/2 scotsquart
choppin := 1/2 scotspint
mutchkin := 1/2 choppin
scotsgill := 1/4 mutchkin
scotsbarrel :=8 scotsgallon
// Scots dry capacity measure
scotswheatlippy := 137.333 britishinch^3 // Also used for peas, beans, rye, salt
scotswheatlippies := scotswheatlippy
scotswheatpeck :=4 scotswheatlippy
scotswheatfirlot := 4 scotswheatpeck
scotswheatboll :=4 scotswheatfirlot
scotswheatchalder := 16 scotswheatboll
scotsoatlippy := 200.345 britishinch^3 // Also used for barley and malt
scotsoatlippies := scotsoatlippy
scotsoatpeck := 4 scotsoatlippy
scotsoatfirlot :=4 scotsoatpeck
scotsoatboll := 4 scotsoatfirlot
scotsoatchalder := 16 scotsoatboll
// Scots Tron weight
tronpound := 9520 grain
tronounce := 1/20 tronpound
trondrop := 1/16 tronounce
tronstone := 16 tronpound
// Irish liquid capacity measure
irishgallon :=217.6 britishinch^3
irishpottle :=1/2 irishgallon
irishquart := 1/2 irishpottle
irishpint := 1/2 irishquart
irishnoggin :=1/4 irishpint
irishrundlet := 18 irishgallon
irishbarrel :=31.5 irishgallon
irishtierce :=42 irishgallon
irishhogshead := 2 irishbarrel
irishpuncheon := 2 irishtierce
irishpipe := 2 irishhogshead
irishtun := 2 irishpipe
// Irish dry capacity measure
irishpeck := 2 irishgallon
irishbushel :=4 irishpeck
irishstrike :=2 irishbushel
irishdrybarrel := 2 irishstrike
irishquarter := 2 irishbarrel
// English Tower weights, abolished in 1528
towerpound := 5400 grain
towerounce := 1/12 towerpound
towerpennyweight := 1/20 towerounce
// English Mercantile weights, used since the late 12th century
mercpound := 6750 grain
mercounce := 1/15 mercpound
mercpennyweight := 1/20 mercounce
// English weights for lead
leadstone := 12.5 lb
fotmal := 70 lb
leadwey := 14 leadstone
fothers := 12 leadwey
// English Hay measure
newhaytruss := 60 lb // New and old here seem to refer to "new"
newhayload := 36 newhaytruss // hay and "old" hay rather than a new unit
oldhaytruss := 56 lb // and an old unit.
oldhayload := 36 oldhaytruss
// English wool measure
woolclove := 7 lb
woolstone := 2 woolclove
wooltod := 2 woolstone
woolwey := 13 woolstone
woolsack :=2 woolwey
woolsarpler := 2 woolsack
woollast :=6 woolsarpler
//
// Ancient history units: There tends to be uncertainty in the definitions
// of the units in this section
// These units are from [11]
// Roman measure. The Romans had a well defined distance measure, but their
// measures of weight were poor. They adopted local weights in different
// regions without distinguishing among them so that there are half a dozen
// different Roman "standard" weight systems.
romanfoot :=296 mm // There is some uncertainty in this definition
romanfeet :=romanfoot // from which all the other units are derived.
pes := romanfoot // This value appears in numerous sources. In "The
pedes := romanfoot // Roman Land Surveyors", Dilke gives 295.7 mm.
romaninch :=1/12 romanfoot // The subdivisions of the Roman foot have the
romandigit := 1/16 romanfoot // same names as the subdivisions of the pound,
romanpalm :=1/4 romanfoot // but we can't have the names for different
romancubit := 18 romaninch // units.
romanpace :=5 romanfeet // Roman double pace (basic military unit)
passus := romanpace
romanperch := 10 romanfeet
stade := 125 romanpaces
stadia := stade
stadium := stade
romanmile :=8 stadia // 1000 paces
romanleague := 1.5 romanmile
schoenus := 4 romanmile
// Other values for the Roman foot (from Dilke)
earlyromanfoot :=29.73 cm
pesdrusianus := 33.3 cm // or 33.35 cm, used in Gaul & Germany in 1st c BC
lateromanfoot := 29.42 cm
// Roman areas
actuslength := 120 romanfeet // length of a Roman furrow
actus := 120*4 romanfeet // area of the furrow
squareactus := 120^2 romanfeet^2// actus quadratus
acnua := squareactus
iugerum := 2 squareactus
iugera := iugerum
jugerum := iugerum
jugera := iugerum
heredium := 2 iugera // heritable plot
heredia := heredium
centuria := 100 heredia
centurium :=centuria
// Roman volumes
sextarius := 35.4 in^3 // Basic unit of Roman volume. As always,
sextarii := sextarius // there is uncertainty. Six large Roman
// measures survive with volumes ranging from
// 34.4 in^3 to 39.55 in^3. Three of them
// cluster around the size given here.
//
// But the values for this unit vary wildly
// in other sources. One reference gives 0.547
// liters, but then says the amphora is a
// cubic Roman foot. This gives a value for the
// sextarius of 0.540 liters. And the
// encyclopedia Brittanica lists 0.53 liters for
// this unit. Both [7] and [11], which were
// written by scholars of weights and measures,
// give the value of 35.4 cubic inches.
cochlearia := 1/48 sextarius
cyathi := 1/12 sextarius
acetabula := 1/8 sextarius
quartaria := 1/4 sextarius
quartarius := quartaria
heminae := 1/2 sextarius
hemina := heminae
cheonix := 1.5 sextarii
// Dry volume measures (usually)
semodius := 8 sextarius
semodii := semodius
modius := 16 sextarius
modii := modius
// Liquid volume measures (usually)
congius := 12 heminae
congii := congius
amphora := 8 congii
amphorae := amphora // Also a dry volume measure
culleus := 20 amphorae
quadrantal := amphora
// Roman weights
libra := 5052 grain // The Roman pound varied significantly
librae := libra // from 4210 grains to 5232 grains. Most of
romanpound := libra // the standards were obtained from the weight
uncia := 1/12 libra // of particular coins. The one given here is
unciae := uncia // based on the Gold Aureus of Augustus which
romanounce := uncia // was in use from BC 27 to AD 296.
deunx := 11 uncia
dextans := 10 uncia
dodrans := 9 uncia
bes := 8 uncia
seprunx := 7 uncia
semis := 6 uncia
quincunx := 5 uncia
triens := 4 uncia
quadrans := 3 uncia
sextans := 2 uncia
sescuncia := 1.5 uncia
semuncia := 1/2 uncia
siscilius := 1/4 uncia
sextula := 1/6 uncia
semisextula := 1/12 uncia
scriptulum := 1/24 uncia
scrupula := scriptulum
romanobol := 1/2 scrupula
romanaspound :=4210 grain // Old pound based on bronze coinage, the
// earliest money of Rome BC 338 to BC 268.
// Egyptian length measure
egyptianroyalcubit := 20.63 in // plus or minus .2 in
egyptianpalm := 1/7 egyptianroyalcubit
epyptiandigit := 1/4 egyptianpalm
egyptianshortcubit := 6 egyptianpalm
doubleremen := 29.16 in // Length of the diagonal of a square with
remendigit := 1/40 doubleremen// side length of 1 royal egyptian cubit.
// This is divided into 40 digits which are
// not the same size as the digits based on
// the royal cubit.
// Greek length measures
greekfoot := 12.45 in // Listed as being derived from the
greekfeet := greekfoot // Egyptian Royal cubit in [11]. It is
greekcubit := 1.5 greekfoot// said to be 3/5 of a 20.75 in cubit.
pous := greekfoot
podes := greekfoot
orguia := 6 greekfoot
greekfathom := orguia
stadion := 100 orguia
akaina := 10 greekfeet
plethron := 10 akaina
greekfinger := 1/16 greekfoot
homericcubit := 20 greekfingers // Elbow to end of knuckles.
shortgreekcubit := 18 greekfingers // Elbow to start of fingers.
ionicfoot := 296 mm
doricfoot := 326 mm
olympiccubit := 25 remendigit // These olympic measures were not as
olympicfoot := 2/3 olympiccubit// common as the other greek measures.
olympicfinger := 1/16 olympicfoot// They were used in agriculture.
olympicfeet := olympicfoot
olympicdakylos := olympicfinger
olympicpalm := 1/4 olympicfoot
olympicpalestra := olympicpalm
olympicspithame := 3/4 foot
olympicspan := olympicspithame
olympicbema := 2.5 olympicfeet
olympicpace := olympicbema
olympicorguia := 6 olympicfeet
olympicfathom := olympicorguia
olympiccord := 60 olympicfeet
olympicamma := olympiccord
olympicplethron := 100 olympicfeet
olympicstadion := 600 olympicfeet
// Greek capacity measure
greekkotyle := 270 ml // This approximate value is obtained
xestes := 2 greekkotyle // from two earthenware vessels that
khous := 12 greekkotyle // were reconstructed from fragments.
metretes := 12 khous // The kotyle is a day's corn ration
choinix := 4 greekkotyle // for one man.
hekteos := 8 choinix
medimnos := 6 hekteos
// Greek weight. Two weight standards were used, an Aegina standard based
// on the Beqa shekel and an Athens (attic) standard.
aeginastater := 192 grain // Varies up to 199 grain
aeginadrachmae := 1/2 aeginastater
aeginaobol := 1/6 aeginadrachmae
aeginamina := 50 aeginastaters
aeginatalent := 60 aeginamina
atticstater := 135 grain // Varies 134-138 grain
atticdrachmae := 1/2 atticstater
atticobol := 1/6 atticdrachmae
atticmina := 50 atticstaters
attictalent := 60 atticmina
// "Northern" cubit and foot. This was used by the pre-Aryan civilization in
// the Indus valley. It was used in Mesopotamia, Egypt, North Africa, China,
// central and Western Europe until modern times when it was displaced by
// the metric system.
northerncubit := 26.6 in // plus/minus .2 in
northernfoot := 1/2 northerncubit
sumeriancubit := 495 mm
kus := sumeriancubit
sumerianfoot := 2/3 sumeriancubit
assyriancubit := 21.6 in
assyrianfoot := 1/2 assyriancubit
assyrianpalm := 1/3 assyrianfoot
assyriansusi := 1/20 assyrianpalm
susi := assyriansusi
persianroyalcubit := 7 assyrianpalm
// Arabic measures. The arabic standards were meticulously kept. Glass weights
// accurate to .2 grains were made during AD 714-900.
hashimicubit := 25.56 in // Standard of linear measure used
// in Persian dominions of the Arabic
// empire 7-8th cent. Is equal to two
// French feet.
blackcubit := 21.28 in
arabicfeet := 1/2 blackcubit
arabicfoot := arabicfeet
arabicinch := 1/12 arabicfoot
arabicmile := 4000 blackcubit
silverdirhem := 45 grain // The weights were derived from these two
tradedirhem := 48 grain // units with two identically named systems
// used for silver and used for trade purposes
silverkirat := 1/16 silverdirhem
silverwukiyeh := 10 silverdirhem
silverrotl := 12 silverwukiyeh
arabicsilverpound := silverrotl
tradekirat := 1/16 tradedirhem
tradewukiyeh := 10 tradedirhem
traderotl := 12 tradewukiyeh
arabictradepound := traderotl
// Miscellaneous ancient units
parasang := 3.5 mile // Persian unit of length usually thought
// to be between 3 and 3.5 miles
biblicalcubit := 21.8 in
hebrewcubit := 17.58 in
li := 10/27.8 mile // Chinese unit of length
// 100 li is considered a day's march
liang := 11/3 oz // Chinese weight unit
// From Encyclopedia Dictionary of the Bible
chomer := 21/2 bushels
letech := 1/2 chomer
ephah := 1/5 letech
seah := 1/3 ephah
gomer := 3/10 pecks
cab := 1.86 quarts
kor := 97.5 gallons
bath := 9.8 gallons
hin := 1.62 gallons
log := 1/12 hin
artaba := 1.85 bushels
chenice := .03 bushels
metretes := bath
// Medieval time units. According to the OED, these appear in Du Cange
// by Papias.
timepoint := 1/5 hour // also given as 1/4
timeminute := 1/10 hour
timeostent := 1/60 hour
timeounce := 1/8 timeostent
timeatom := 1/47 timeounce
// Given in [15], these subdivisions of the grain were supposedly used
// by jewelers. The mite may have been used but the blanc could not
// have been accurately measured.
mite := 1/20 grain
droit := 1/24 mite
periot := 1/20 droit
blanc := 1/24 periot
// Resolution 12 of the BIPM 21st Conférence Générale des Poids et Mesures
// 11-15 October 1999 endorses uses of katal as SI derived unit:
// http://www.bipm.org/enus/2_Committees/cgpm21/res12.pdf
katal := mol/s
kat := katal // SI symbol for katal
// Some silliness:
smoot := 5 feet + 7 inches // Height of Oliver R. Smoot Jr. see:
// http://spectrum.lbl.gov/www/personnel/smoot/smoot-measure.html
//
// Some definitions using ISO 8859-1 characters
//
//¼- 1/4
//½- 1/2
//¾- 3/4
//¢ cent
//£ britainpound
//¥ japanyen
//ångström angstrom
//röntgen roentgen
//°C degC
//°R degR